It is not really cheating if you are not lawfully married to this guy. Even if you were lawfully married and he was having sexual relations with another person, you couldn't really "sue" him for cheating -- all you could do is file a Complaint for Divorce against him based on adultery. However, without being lawfully married, there is no grounds for a divorce based on adultery because: (1) there is no marriage to be dissolved and (2) adultery is defined as having sexual relations with someone other than one's spouse (since there is no spouse, there is no adultery).
As the prior attorney stated, you can pursue him for child support for the two children that you are already have. You will not be able to file for child support for the third child until after the child is actually born.
You can pursue child support one of two ways: (1) file a petition for child support with the Juvenile & Domestic Relations District Court in the county in which you and the children reside OR (2) you can contact the Division of Child Support Enforcement and file an application for services with them. If you go through the court, then what you will get is a judicial order for child support which the Div. of Child Support Enforcement can then enforce for you through wage withholding. If you go through the Division instead, then what you will get is an administrative support order which will be enforced by DCSE (but is subject to appeal to the courts). DCSE is VERY busy (over-worked and under-funded/under-staffed). So, it may take several months longer to pursue the administrative support order process through DCSE and the J&DR Court will probably be faster for you.
If you want to pursue through DCSE, then you will need to find out where your particular district office of DCSE is and then schedule an appointment with them (some, like Fairfax County, have certain days of the week or the month when they take walk-ins, but the lines can be long, so go early). If you want to pursue through the court, then contact your local J&DR Court (which, unless you live within the City of Alexandria limits, is probably Fairfax County J&DR Court). The court will schedule an intake appointment for you at the court.
One final note in reference to your tag "Back Child Support": Child support can NOT be ordered retroactively, but only from the date on which a petition for support is pending. What this means is that the clock won't start ticking on child support until the day that your petition for child support is filed with the court. (Administrative support orders are subject to the same limitations as judicial support orders). So, if you want and/or need child support from the children's father, then you need to file as soon as possible. Every day that passes where you have not filed is a day for which you can never recover child support!
This response does not create an attorney-client relationship and is intended for general information purposes only.