Hi mariposa, I am sorry to hear this latest turn of events. Dr Harley has very specific advice when there is an OC [other child] involved. The first, and most ideal, option is that your H agree to never see the child or the OW again. If eliminating the child from your lives can't be done, then all communications regarding the child should be transmitted via a 3rd party for life. Neither of you should ever have any contact with the OW for life. If it were me, I would make it a condition that he NEVER see the child in order to continue in the marriage. Reason being, every time you see the child, you will be reminded of the affair. It is a nightmare existence for most. In marriages where there is no contact with the OC, the recovery is much, much healthier and complete.
The basic principle is that the marriage and the children of marriage must be protected first and having an OC and OW hanging around jeopardizes the marriage.
Secondly, having a baby daddy hang lurking around makes it harder for the OW to find a husband who can father the child. So everyone benefits when Baby daddy just hits the road.
For your current situation, I would suggest a few things. First off is to NEVER EVER allow your own children to be exposed to his filthy, vile affair. He is teaching your children to be as immoral and corrupt as HIMSELF and you can't have that. So, don't allow your children to visit him unless it is without skanky. PERIOD.
I would get that issue settled TODAY. NOW. And tell your children that their dad is leading an immoral, corrupt lifestyle. The moral confusion they feel must be enormous. They know this is wrong yet they have adults telling them that wrong is right.

They shouldn't be put in a position to have to figure out right from wrong in their 30's by reading books because their parents failed in their duty.
Next step would be to file for divorce and get legal protection. You are in a very precarious legal situation with the OC situation. If the OW filed for child support, her child will have first dibs on CS and yours will come SECOND. So get legal protection and tell your lawyer to put in the papers that your children are never to be exposed to his affair partners.
After you clear the matter of the visitation [do this today] I would work on going into Plan B as soon as you can. Get an intermediary, arrange child exchanges, separate bank accounts, etc. Read through this and get all your ducks in a row:
here