The only person that knows when to start potty training is your son. You are absolutely right about it not being ideal to potty train at a time when there is big change. We moved from the US to here a week after my sons 2nd birthday. His doctor told me to not even think about potty training until we get settled and a new routine established here. Before we moved I would just talk a lot about using the potty, but never ask him to try. I would ask him if he could find the potty and he would run into the bathroom and point to the toilet (it was a game). I would tell him that the potty is where his pee-pee and poo-poo (sorry, hehe) would go when he is ready. And we watched Elmo's Potty Time DVD all day, everyday and read potty books. When we moved here I never pushed him, because we were only here for a few weeks. Then he walked up to me and said, "oh no, mommy, pee-pee potty." I knew he was ready because I listen to him.
With big events (new baby) I think it is best until they are settled, but don't under-estimate your son's ability to adjust to change because they can sure surprise you (like mine did)! My situation worked well for me. I knew there was going to be a big event (moving) so all I did was talk a lot about the potty to educate him and try to make it really fun. Then I let him tell me when he was ready. If your son is 3 years old when he is ready, then so what. There is a lot happening in your household. I know what you mean with the pressure from your in-laws, but that wouldn't convince your son to start potty training and he is the one with the final say. I have had friends who pushed potty training before their child showed signs of being ready and it is traumatic!
To sum up, you know best. The "potty talk" is a great way introduce potty training without actually starting (which might satisfy your in-laws) then wait for your son's cues to tell you when to start. This is just my suggestion from my personal situation. Every situation is different, so I hope it might of helped, if even a little bit. Good luck!!