Hi Nino,
The other mamas have given great advice. Your marital status won't matter in a custody fight. It's not about who would be a better "mom".
But I have a question - you say that the biomom "keeps him away from us even though he is supposed to get everyother weekend, once during the week, and every other holiday".
Do you have a formal custody agreement in place - filed with the state?
If your bf is supposed to get his son, THEN HE GOES TO THE HOUSE AND GETS HIS SON. If the biomom doesn't hand over the kid he calls the police and a lawyer, shows them the custody agreement, and she is in contempt of court.
HE WILL NEVER GET CUSTODY IF HE IS NOT EVEN TAKING HIS SON THE MINIMUM AMOUNT OF TIME THAT HE CURRENTLY HAS AVAILABLE. The ex will go infront of the judge and lie and say that the biodad doesn't take him for visits.
So that is were he MUST start. If you DON'T have a custody agreement filed in court then he MUST do this TODAY. It is the only legal protection he has to see his son.
As far as moving - most states say that you can move no more than 45-60 miles from the current address without letting the other parent know 60 days before the move. When she lets you know, he contests and then SHE CAN'T MOVE WITH THE BOY.
Good Luck.