I've had family sims with all adult children get the want, and most sims start wanting grandkids after their first one, but it's not strong enough to run over the standard adult wants like the elder tree.
I've started to get annoyed with Family Sims who suddenly DON'T want babies the moment they get hitched (Dustin Pleasant, you who changed aspirations at Uni, that means you!). The only person in that family who wanted a baby at that time was romancer Daniel Pleasant wanting a grandchild. And NOW Dustin decides he wants a baby.
Jeeves, Cass Goth wanted babies every time she turned around! Thankfully she's hit menopause and has stopped nagging me about it - you've got four children, plus two stepchildren from Darren (Darren's alien baby girl, Darian, plus Dirk), deal with it!