It's hard having this situation, I am sure. My husband and I are going through the pre-stages of that. He wants to have a child, and I can't even handle his daughter right now. The thing is, we have her half of the time. Her mother is a very negative influence and I won't even get in to that, the court orders, etc. But, my SD (11yo) is very negative and even threatening at times when this is a topic.
So, I would say, keep it quiet for your health and the baby's, and of course, the lack of unnecessary stress for as long as you want to. Then, I suggest bringing the idea in gradually. Talk about it around SS, then do little things to acquaint him with his new sibling's arrival. Also, my counselor and I talked about that idea that - if you make you SS important to the role of big brother, he may respond a little better. If he can be a "big helper" and be proud like a dad, it may give him more positive feelings toward the baby. Also, let him pick out a toy or clothes or something for the nursery so he feels like a part of the process, not something that is just competing for his attention.
If BM is giving you a hard time or your SS, tell you SS that this child is a blessing, as all children are, just like him. That way, his mom can't say otherwise, and you can also say, I'm sure I'm just as lucky to have this baby as your mom was to have you. What mother isn't fortunate to have a child? Also, remind him that this baby is a blessing to him too. (Even if it's not the case now with his behavior) remind your SS that this is his blessing too! He will be a big brother with someone who will admire him and look up to him. That he has this special role and he is lucky to have that because some people don't get to be a big brother and have such an admirer. Just suggestions...hope they help you, or at least spark other ideas for you. I wish you the best!
Take care!