Child support and Visitation

Rosemary, you know he gets paid under the table. Make your lawyer aware of this. If he is self employed and you know how much he makes then they will set it on his estimated income , including bonuses. You know how much he has made when you were "together" and that is who much he should report. IF it is court ordered..then he will have to pay it regardless of what you do or if you are seeing someone.
As for the visitation..it can be set so that you both agree. And if it is worded right, you  will have some control over it. Have it put in there that you can't have overnight guests of the opposite sex while the children are with you.
Without court appointed document he won't have to pay you anything if he so chooses and you can't make him! And if you let him "see" the kids and he would decide to "fly the coop" you have no legal leg to stand on to get them back.  Read some of the blogs in here..it happens more than we know!
You need to have a legal document stating such things for him and you to abide by. You have too much to lose without one.I am putting a link on this post for you to look at. Read some of the horror stories in here and you will see what I am talking about. It is just not worth it~
http://docs.google.com/View?docid=dc876ktm_9d4mq6f2s
Spaznskitz, a family law attorney, wrote this to head off any issues in visitation and child support. This is one that she uses for her clients.

We haven't started anything legal he is stalling hoping the he can win me back.  He has massive on-going long term issues with child support enforcement so as long as I'm "fair" he'll probably be descent.  The problem is as soon as he accepts it's over or I start dating some else he'll stop paying.  But If I to go through court enforced child support I more then likely receive nothing.  He is a plumber and can spend the rest of his career working under the table or limiting his income.  The man makes at least $80.00 on hour with regular bonuses.  He cheated on me and has a child with someone else.  The year they went to court for child support he made about $550,000 and he only has to pay $178.00 a month to her.  I pretty much accept I will not get constant support and I would rather have some control over visitation.  So maybe it's better if I don't file with an official agency.  Without court appointed instruction what can he really do.

But you can get in deep doo-doo if he has ordered visits and you don't let him have them!

From all I read YES you have to honor his visitation. You cannot withhold the kids from him because of that. I am assuming you have court ordered visits?
Child support is decided by taking both incomes and figuring insurance, child care etc if applicable. Search online for a child support calculator for your state. You can put the numbers in and it will give you a ballpark. He will only have to pay for kids that are his with you and if he has adopted yours.
I would start by garnishing his wages..if he has a job. Get the court to set your support . I am afraid you may have a man who won't pay. It makes no difference who files first but it is according to income, health insurance etc. If you receive support for kids that are only yours, there is a place to put that also.