Dating my husband during separation
You CAN see people, of course, but use your best judgment. Again, once you've signed a separation agreement, it's less risky–but it's still adultery (and therefore still a misdemeanor in Virginia) until you've got that Final Decree of Divorce with the judge's signature on it. I would say, however, that if you would be angry with your husband for having his new girlfriend over while the children are there, then it would probably be a good idea if you didn't do it either.
Before you've signed an agreement, it's a very bad idea. Until there is an order preventing you from doing something (like having unrelated overnight guests when the children are present), legally speaking you are allowed to do it. It's probably also not a bad idea to consider your children and where they are in the whole process.
This is why you may want to be careful who you date and who you get serious about during a divorce.
This is true even when your spouse is the one who left the relationship and wanted a divorce.
It is worth you considering whether dating during a divorce (especially if you have a spouse with poor anger management skills or one that is vindictive) can wait and whether it is best to not take an already difficult situation such as a divorce and make it a bit more complicated by bringing in a third person into your life.
Whenever you start a new relationship before you've finished the old one, there's a risk.
That is especially true when your old relationship was a marriage.