All children have some difficulty but some have more difficulty than others when they go back and forth between parents and 2 different styles of living and parenting. My 3 yo grandson is whiney and cries alot the first evening he gets home. He cries and asks for his dad all week. He misses he dad. He has had some play therapy and his mother has received some parenting tips which have improved his behavior noticeably. I think that he lifestyle at each home is similar.
But it sounds like there is a big difference in your son's case. His father having a new wife and 4 kids would be upsetting. That is a lot of change to have to adjust too. And there may be tension between his dad and his wife over the children. It is quite likely that some of the things he wants to do he is able to do at his dad's. How do he and your other son describe life with their dad?
I'd also recommend talking with your ex and see if you can agree on some basic rules that are healthier than candy to be followed at both homes. And it would help for both of you to exchange a list of rules that are enforced in each house. The wife may be better able to help you with this. It will help tremendously if you know what the rules actually are at his house even if you don't agree with them. As it stands now everything except the unwanted behavior is vague.
Another important thing to consider is are the children treated with respect and do the adults talk of the other parents with respect. When kids sense a lack of respect they will respond negatively.
Another idea is that they may be unhappy going to their dads house and are acting out instead of telling you. They may not even be aware of their actual feelings about any of this. They're unhappy and this is how they show it.
A conversation about feelings and how to handle them might help. There are some good books for that. I've found some in the library and I've purchased some. If you're interested I can send you the titles and author names.
