the fact he hasnt paid anything towards your children wont matter if the reason you are taking him to court is for the sale of the house etc, if you bring that up they may think you are using any old excuse, my friend was in the same situation nearly,
i doubt you would get away with only giving him 10k as im sure the house costs more and as you are married and joint owners you would be very lucky, get onto the csa for maintenance , if he lives with a new partner and her child he will have a percentage of his wages taken off before the assess him for this other child