I'm in SC. Did you file fault or no-fault? Were you legally separated with papers on file with the court? If so, is there any language in the legal sep. papers that say something to the effect that "both parties shall live as single and neither party will hold the other responsible for ..." ?
If he's still a legal resident of this state, yes he's committing adultery. Whether a judge would care at this point is unknown, and a judge is definitely not going to use *someone else's* fb posts as proof of it.
Furthermore, since you've met the legal requirements to file for no-fault in this state, going for fault is fairly well pointless unless you think you're entitled to a huge alimony payment. Those are not a given in ANY situation because of a lot of factors, not limited to:
1. Length of the marriage. (a couple of years won't cut it)
2. Need of the receiving party. (you've been without his income for the last year (?) )
3. Income of the payor. (you can't get blood out of a turnip)
Child support for 3 kids will certainly be ordered, so he'll be obligated to help you support his kids. If the marriage is over however, and with the limited info you've shared, he is not obligated to help support you.
Best advice I can offer is to get a couple of free consultations with family law atty's in your area. KEEP IN MIND: Lawyers are in the business to make $$$$ - one that promises you the moon better have a track record of DELIVERING it to other clients. Research their track record before hiring one - with him in another state and you with 3 kids to support, the last thing you need to do is pay big $$ to a fast-talking lawyer with no clue.
Marriage doesn't come with a money-back guarantee.