Esme is the custodial parent and she agreed to coparent with Spencer along with Laura's supervision.
Nicholas may be the father -- though it has not been proven. He's a fugitive from the law for heaven's sake. He can't disappear for months to avoid the law, come back into town and take Ace adding kidnapping to his charges.
In fact, Nicholas could well be charged as an accomplice to kidnapping for handing Ace over to Nicholas. And if Spencer thinks Esme is going to take this sitting down, he clearly isn't using the few braincells the writers currently allow him to show.
Karen L.