Hi L.,
I have two sons and two grandchildren (one 3 years and the other 11 months). With my boys and the grandchildren, I found that I had to pay close attention to what's going on with each of them. You are likely very busy especially with a 3 month old and a 3 year old. You've got to find the time to really see what's happening. Various things could be going on (jealousy, need more attention, some fear brought on by something that happened or was said,...). Several months after the 11 month old was born, the 3 year old decided that she didn't need to use the potty and went back to using her pull up. She was a little jealous of the baby and needed a little more attention. We began emphasizing to her that it was not okay to use the pullup and began really praising (high fives, hugs, and kisses) her when she used the toilet. We let her see our disappointment when she didn't (sad face) and encourage her. She began using the toilet and coming all excited to report that she had done so. We also did things to help her be a part of what we needed to do for the baby. Now she's in regular underwear and becoming the "big sister" for her baby brother. With my older son, when he started potty training he would have an accident sometimes and didn't seem to mind that he was wet. One time, I didn't change him immediately and let him know that he couldn't sit on me or the sofa or whatever so that he could see that it means more than he is wet and needs to be changed. After that he had no more problems paying attention. That worked for him. I don't have an answer to the problem. You have to discover what's going on with your son and what will work best for him.
Best wishes
E.