I have a dog aggressive dog, and he has caused me far more stress than having 2 babies.
My advice is to return him to the rehoming centre. They were not honest with you, and should not have placed a dog with issues in an inexperienced home. If you do plan on keeping him find a dog behaviourist. Ask a vet for a recommendation. You need more than a 'trainer', as pretty much anyone can call themselves that.
Dog aggressive dogs are usually fearful and submissive by nature, with aggression being a defensive reaction to the fear that the other dog will hurt them. Not aways, but this is a very common reason. A fearful dog needs a confident owner, who they feel will take control. The dog will be picking up on your anxiety and that will be making his behaviour much worse.
I reacted in a similar way when we first got our dog aggressive dog. I would inwardy tense up and get nervous if I saw off lead dogs approaching, anticipating a fight. This made our dog's behaviour much worse. My DH however dealt with it differently, he didn't get stressed, he managed the situation, and our dog is much more relaxed and less likely to kick off when with him.
Some tips.
When out for a walk, if you see a dog approaching simply turn around and walk away. Break the dogs' eye contact. Use tasty treats with a strong smell like bits of sausage and talk posiively to your dog. Then turn back and walk back towards the other dog until you feel him start to react. Repeat above. Work up to the point where you feel you can walk him past another dog over time. It is important to keep your dog within his comfort zone.
If you know someone with a friendly dog try some practise walks using treats, distraction, and walking away, to get your dog comfortable. Avoid situations where the dogs have eye contact.
Build a bond with your dog through daily training session. Teach commands such as sit, down, touch (touching nose on your palm when you hold your hand out to your side. Teach this by putting small piece of hand between your fingers so he has to touch your hand with his nose to get it). Touch is the most useful command to know because if you want to call your dog, rather than shouting which can stress a nervous dog you simply need to hold your palm out to the side.
Also Post in The DogHouse on here. There are some very knowledgeable people on there who will be happy to help.
The baby issue, I can see your DH's concerns. You do need to get the dog's behaviour under control before having a baby. A dog aggressive dog is dangerous because they are usually in panic mode, A panicked dog is not safe around children.
For context my dog bit me on the leg once, because my leg was between him and the other dog. He was going for the other dog, he didn't mean to bite me, I was simply in the way. A dog's mouth is the height of a child's face. Think about it.
Similarly, my dog bit the side of the pram with some force. Again it was a case of the pram being between him and the other dog. I am forever grateful that it was the side of the pram and he wasn't round the front. That was the last day I walked him with my dcs.
I am fortunate that I do not have to walk him with the dcs as we have a field and I can exercise him there with a ball. If walking with a pram is your only option you can't consider this if he is unsafe. Muzzles are not an answer either, as aside from making a nervous dog more nervous, a muzle punch from a dog in attack mode can do a lot of damage to a baby.