My kids are half British half Japanese, living in Japan where nothing short of 100% Japanese blood will forever make them “foreigners”.
Both of them have had their troubles, the elder more than the younger in that it hurt him more. We also found a very safe small village school for them so the younger one has benefitted from never having been in the big public school at all.
The elder one went through a phase at around 6-9 years old of wanting me to come to kindy/school open days then telling me I wasn’t to open my mouth so they wouldn’t know I’m not Japanese. Good luck with that one kid… He also had a bit of a fit about “don’t stand with me so people won’t think you are my mother” in public places like the zoo or other days out. My husband got very angry and upset about that and told him to go and find another mother if he didn’t like the one he’s got, and that tailed off fairly quickly.
That said, now at 13 the elder one is a very balanced “half” and truly cannot say which he is more, Japanese or English. He is very proud of his both-ness and he plays it off as cool, which most of the kids in his new JHS are falling for. He gets some snide comments but he just laughs them off as jealous or ignorant.
The younger one is pretty much Japanese in nature, language skills and attitude but oddly he looks very much more western - at nine he still is blond-ish. He on the other hand has never had any problems with me being English in his school or in public, but he relentlessly uses Japanese with me these days because it’s easier (and he thinks that anything Japanese is better - he’s totally bought that cultural gem!)
On the other hand he’s at the stage of thinking very deeply about his family and how it’s made up. Many conversations are had about our DNA and who contributed what, and how. He attributes culture to DNA too which is funny. I just got informed last night that it’s Mummy’s DNA that lets us decorate the Christmas tree each year!
We do have a lot of small family traditions that are simply just ours. Not specially English (though we have Christmas etc) and not specially Japanese (though we have 7-5-3 etc) but just ours. All kids love small family rituals and it’s part of what makes us a unit, against the rest of the world!
Some of ours - decorating the Christmas tree together no matter what. My husband lives away and we always save it for a day he can be with us. He stayed extra late last weekend so my elder son could get back from school to do it together. We eat sushi for every birthday and exam success in the family. The tooth fairy comes to our kids but leaves the teeth under the pillow so they can be thrown in the proper Japanese manner the next morning. The kids don’t get new year’s money but they get lots of Christmas presents, not just one. I can’t remember many of the small rituals we have but there are a lot, some that the kids made up themselves but they serve to bind us together and make up our own culture that is unique to our family.
It sounds like that is the sort of thing you need to be working on to make your new family stick. Trouble is some of these just come from time together and some can be “manufactured”.
But yes, to have pride in where you are from AND where you are going is a big thing, and I’m glad that you are happy to address this with your new kids. I do wish you a lifetime of happiness together!