It’s not quite the same situation, but my parents always treated my son’s half-sister (not genetically related to me or them as their granddaughter. That was partly because they didn’t want to create contention between my son and his sister, and partly because the kids’ three actual parents, including me, were being fuckwits during their early youth.
I’m not quite sure I understand you. In the Netherlands, asking someone to be the godparent to your child is no longer a just a religious thing, either. I wanted a good friend of mine (an ex, actually) to be in my childs life, so I asked him to be the kids godparent and he said yes and that was that. 
We’re all atheists. I just figured that being a godparent is a good way to make yourself more “related” to a child, if you should want that.
I think it’s becoming less of religious thing here, too. I didn’t realize that you were suggesting the OP could fill that role.
Let me tell you about my “Grandpa”.
He was a divorced sailor with no children of his own who met a “cute dame” after the war. She was a war widow herself, with a sort of stubborn, spoiled boy. He married the woman eventually, but things were tough with this spoiled 13 year old who had grown up with his grandmother and mother and a house full of aunties. It was tough times all around, but the marriage was for better or worse and they managed.
When the spoiled kid grew up and married and had Mona Lisa Simpson, Grandpa found his role in life. He wasn’t a step anything, he was MY GRANDPA. My brother, a few years younger actually says “weekends and holidays, he was my dad”
I gave the eulogy at his funeral.
But, your milage might vary. Except for my brother and I, Grandpa would never have had children in his life. Also his sisters and brothers sent gifts for my family at Christmas and other occasions. I still refer to having family in Prince Edward County, although there is no “blood” connection.
I should also tell you the experience with my Beau’s family.
My Beau is adopted. He has an older sister and two younger brothers that are biological children of his (French Canadian Roman Catholic strict) parents.
The older sister has one son. The Beau has an out of wedlock child we never see, (that’s a long and sad story, we are hoping things change this year when the girl turns 18) and of course he is “dad” to my seven year old son. (My son doesn’t remember the Beau not living with us)
The next older brother has four children from two different marriages. He has almost no contact with the first child, and is just recently split and very involved in the lives of the three others. The youngest son is living with a woman who has three children from a former marriage, and they together have one son.
His father has pictures of “all my 11 grandchildren” up on the wall over the tv set. The first Christmas I spent with his family (a year and a half after the Beau and I started living together) I was walking around crying all the time about how inclusive and wonderful this family is to me and my son.
Other than my actual Mother In Law, that family did more for my son that first year than the biofamily has done in seven. (My mother in law is wonderful, not her fault her son hasn’t picked up a phone in 6 and a half years)
Families are what you make them, you can be nice polite and distant or you can be as involved as you want. Just remember children don’t ask to be born to create drama, and take your cue from your daughter.
I am worried that your daughter is not getting enough support from her family in this case. You all seem to think she’s being stupid and sentimental, but what would you have her do? Tell her husband to chose between having her or the child in his life? Let him visit the child but never bring him/her to their home? Tolerate the child in her home for visitation but stay uninvolved in the child’s care? Be civil to the child’s face but rant to her family about the horrid injustice of it all?
Assuming he’s not a complete piece of shit, he will want to be in his child’s life. She has to choose between joining him with a whole heart or leaving him. Any middle ground will be insanely more difficult over the long run.
Point taken. My daughter is in a very awkward situation and is standing firmly by her husband’s side. Our family has never dealt with this kind of situation before so everyone is wondering what the appropriate thing to do. We will follow my daughter’s lead. I have told her that we will be “involved” grandparents as much as she wants us to. That’s about all I can tell her at this point in time.
dolphinboy, I have to admire your very gracious responses throughout this thread. You sound like a sincere and reasonable person.
I hope the child gets to know you at least a little bit; you’d be a wonderful example for him or her. 
In my personal opinion family does not have to have anything to do with being blood relations. I grew up in a family that unofficially adopted people into it with extreme generosity. On my own behalf I am now an adoptive sister and aunty to some folks who have no family in this country - we have decided to be family. I guess my point is that your relationship to this child is what you decide it is.
Your daughter must tread carefully, the child has a mother. You and your daughter have no legally recognized relationship to her. You can act in the roles of parent and grandparent, but you have the responsibility not to cross over the lines. If the situation changes in the future, for instance with your daughter becoming a custodial parent, that would be a different situation, but for the time being you have to be careful not to cause conflict with the child’s biological family. Best of luck to you and your daughter, and her husband’s child.
Congratulations. Send footsie pajamas and a stuffed animal.
My first grandchild, whom we believe to be on the way now, will have around seven or eight grandparents, and it breaks my heart that s/he could have three or four more, but won’t.
This child will have so many grandparents because a few people worked hard at creating friendly relationships after divorces, or something similar, because there was a child involved. Some of the grandparents are married to each other, some used to married to each other, some have never been married to each other, and I’m still not sure how one of them fits into the picture.
I will always treasure the memory of my incredibly conservative in-laws welcoming my spouse’s previous spouse’s new spouse to the family.
This is how it has worked in my family.
In my early twenties, I settled down with a man in his thirties who had custody of his two children. We were together for almost nine years before going our seperate ways. Both kids (now adults) still refer to me as their mom and I tend to refer to them as my kids. their dad and I have remained on good terms, mostly because of the kids.
When my son married his ex-wife, she had a three year old son (who immediately stole my heart). Eventually, my son adopted him and the family added my granddaughter. It’s not hard to guess what relationship I have to the little turds that call me Mimi. 
One of the cool parts: the first Christmas that they were married, my son, my dad (who raised a nephew by marriage and a foster son as his own) had a late night discussion one night about raising kids who didn’t share you DNA. My dad gave his grandson some of the same advice that he gave me when I embarked on the journey of step-parenthood.
To make a long story short (I know, too late), LittleBamBam won’t suffer for having another grandparent who loves him. And you will likely get a lot out of the relationship too.
Near-nonissue if he’s never around the step-grandkid… but something to consider if the half brother is around the full siblings on holidays etc. As in, if you’re sending presents to your grandkids for Christmas, and their half brother will be there also, it’d be a really nice thing to do to send him something to open as well. It’d surely mean a lot to him especially in that situation where he might already be feeling left out.
Just sign it “Grandpa Dolphin” or “Uncle Dolphin” or something like that.
Lots of appropriate responses. I’ll just add that, in every case I’ve known where the family accepts a non-biological child as a full-fledged member of the family with no distinctions made about the child’s origin, it’s felt like the right thing and been recognized as a great thing.
My mother’s side of the family, a long line of occasionally cranky people with questionable social skills, were babysitting a neighbor child in the Great Depression when his family took off and never returned for him. Despite the financial crisis, they took him in completely and unhesitatingly, and he was treated just like the rest of the children for his entire life. I didn’t spend much time with him, but everything I’ve heard about him leads me to believe he brought a lot into the family as well, and there have never been any regrets expressed.