Does he like one of the kids more than the other? This sounds very odd to me. usually the courts try to keep siblings together. If one of you has custody of one and one has custody of the other, the kids would rarely get to be in the same place at the same time, they'd miss growing up together. Could he be doing it to avoid paying child support? If you have both kids he will definitely have to pay child support so he may be thinking if you each have one it will be a draw, you each just pay for the one you have. I think it's rather unusual for siblings to live apart unless one chooses to live with the other parent.

Your husband does sound irresponsible and it also sounds like the marriage has been over for a long time. Joint or shared custody sounds like the best idea, you're not taking them away from him but you'd have them primarily and make sure they are taken care of.