I don't think this is a situation you can try to ignore. It seems like he is going out of his way to impress your sister and aside from being totally disrespectful to you it may end up in him putting her in an uncomfortable situation as well.

I also find the idea that he tells your children you hate him off putting. It feels like maybe he is trying to turn them against you or at least bring them to his side.

He should not be involving the children in this at all.

I would definitely suggest couples therapy if you want to try and save the relationship .

Maybe tell your sister. She may be able make sure he knows she is completely uninterested and therefore dampen his interest.

A little less time spent by the two together may help too.