I have 2 boys and just have to say that boys are harder to get finished with the potty training, and maybe at 3 he just doesn't have the capacity to be trained yet. If he is clean and dry, but you find yourself reminding him to go to the potty every few hours..it is really you who are trained and not him.
Some children have more challenges with this that others. Perhaps his diet has changed with the Holidays, maybe he even has some sort of intolerance to something that normally doesn't show itself ( but he's had alot of something lately) and how you are seeing issues with constipation...and now the several accidents a day problem.
I would suggest just getting back to a normal diet as soon as possible, limiting sweets, and observing for a few days. See if you can resist the urge to get him to the potty, and observe if he is having more problems than normal ( could be UTI), is pooping regularly ( if not, the accident problem could be constipation or encopresis) and just be supportive.
Try your best to not be disgusted, frustrated, etc with accidents because it could quite possibly be that he is not mature enough at 3 to be potty trained. With the introduction of a new baby coming, the last thign you want to do is create more of a power struggle and an emotional problem with this. Rest assured, most of this handles itself...just stay calm and not confrontational.