You cannot let your GD and his 'on off 'girl friend suffer for your sons infidelity .My priority would be for them.
Sorry for this but your son behaved very irresponsibly allowing another child into the world unless he was going to commit himself to this other woman, which did not seem to be the case, as it took you so long to find out your son was the biological father. I can understand his' on 'off relationship girl friend feeling you are thinking of your own needs but it is not in your GD's interest to be used as a 'pawn' by her mother so I would put them first or seek professional advice if you are so determined to bring into your life, on a regular basis, this other grandson.
I can't believe my car insurance has risen by that much!