I'm thinking that if someone is that concerned about potential partners fucking up the situation with the kid(s), they should probably not date at all until the kids are grown, or at least old enough to stand up for themselves.
And before someone accuses that of being an "age-ist" remark - no, I don't think it would be the SAME AGE for every child. However, I do think it's important to not place the burden on a child of making adult decisions prematurely. So I would say that a kid becomes "old enough to stand up for itself" somewhere between the ages of 10 and 16. But no, I didn't invent the world and I wasn't handed this age range on stone tablets by a burning bush on top of a mountain in the desert.