I don't know anything about poly relationships, but it seems that if a couple with kids are unhappy in their relationship, and adding another adult fixes their relationship issues, then it would be a positive thing for the kids as well. Ie, kids shouldn't automatically rule out poly relationships. Though I'd agree, having kids with a person outside the marriage could be legally a mess. Then again, single people have kids all the time and have to deal with the messy details of that.
All of the things you're describing involve selfish behavior on the part of the adults. One partner wants this, both want that, but "should" seems to be missing from the equation.