Your dss needs to be aware of his body signals in order for potty training to be effective. It does not sound like he is yet completely aware of his body. One thing you can TRY to help him become more aware is to put him in training underpants with plastic pants over them. When he urinates, he will feel the wetness against his skin (diapers remove the wetness away from a child's skin), which may help your ds become more aware of his body signals.
If your dss seems to be "getting" it, you can continue with the underpants/plastic covers when he is at your house. If he does not get it, or if it's too confusing for him to potty train for a couple of days with you but not with bio mom, then you may need to back off for a couple of months or so before trying again.
Even if your dss DOES potty train now, it will be close enough to when the baby is born that there could be some regression after the baby arrives. You might just mentally prepare yourself for changing two sets of diapers (and be pleasantly surprised if dss potty trains successfully before then).
BTW, nighttime potty training is different. The body must first develop a hormone that tells the kidneys to slow urine production when the body is asleep. Once your dss starts having less wet diapers or occasional dry diapers, then you can begin limiting fluids before bed and take him to the toilet once during the night to help him learn nighttime toilet training skills.
Jesse, Hi and welcome to the Toilet Teaching board.
The previous poster gave some great information. I want to add that he needs consistency or he will get confused. Everyone that watches him needs to be on the same page. To get him to recognize the feeling of needing to go I recommend the naked method. This way he sees what is happening and can start to put it all together. After the baby is born expect to have some regression, as that is natural. It usually takes a month or so for things to settle down and get back on track. I hope that helps. Please keep us updated on your ds progress.