The re-tooled Eight Simple Rules, is going to be a Sob-Com, not Sit-Com, the family is going to be grieving and crying over the Death of the Dad, for a long time.
For me, if they brought Giles from Buffy, to sooth the Widow’s pain, I’d watch, just to see what happens.
They could bring in Dick Sergeant…
Actually, I like the idea of having Anthony Head come in to comfort the widow, AH being the second-hottest male cast member from BtVS.
Where’s my Three’s Company DVD season boxset ? And when is it coming?
Well, hey, they continued doing Three’s Company after Suzanne Somers died.
(yes, i know she didn’t die)
Anyway, they always say “it’s what he what have wanted.” What a show business cliche. What he would have wanted is not to have died in the first place 
Just to clear up some of the references to Valerie/Valerie’s Family/The Hogan Family upthread:
When Valerie Harper left the show in a contract dispute, the producers consulted with fans of the show and asked them how they wanted it to continue. The overwhelming consensus (to the surprise of the producers) was that Valerie’s character should be killed off. This turned out to be a successful move, and the show ran for another three years. Sandy Duncan did not replace Valerie, she was brought in to play an aunt. Although I haven’t watched 8 Simple Rules, it seems to me that a similar approach could work with that show. The Hogan Family did only one episode dealing with Mom’s death, and then moved on, focusing on the kids.
My personal choice is almost always to recast a role, but I know that most fans are horrified at the thought of a recast. I’m not sure how appropriate recasting is when a cast member has died. Besides, Dick Sargent is dead too.
Bring in Anthony Head (Giles)
as a teacher of one of the daughters - it is a new school year. And the mother and teacher throughout the year start getting close, she is still greiving her husband’s death, but the next season (if there is one) a dating situation/relationship can commence.
or
A high school friend that the mother had forgotten about, she grieves for her dead husband during the season, but she finds out that a high school reunion is being planned - which she helps with, hooking up with the old friend. The next season (if there is one) is the high school reunion, and the two old friends start dating.