Ignoring the argument with your ex for a minute, what sort of relationship do you want with your son? A personal story:
My parents split when I was ten, and my mother had primary custody. My father wasnít a horrible person in an objective sense, but he was very much a ďmy house, my rulesĒ kind of person when we I was with him. Whether that was because he had a different set of values from my mom, was naturally an authoritative person, or was himself struggling from the divorce doesnít really matter. What matters is that I was 10, 11, 12, 13 and was really struggling to adjust to my parents split, and had to operate under a different set of rules when I was in his house. It was like walking on eggshells at his house, because Iíd always screw up while I was there, and then the visit would be ruined. Biologically speaking, kids at that age already have trouble with following rules, so having an extra set was frankly too much.
Anyway, it changed over time from me being excited to see my father to me dreading to see my father. And once I became an adult and didnít have to see him, I saw him less and less, and then talked to him less and less, and then I stopped. Iím in my 40s now, Iíve neither talked to him or seen him in over a decade, and I donít really have any regrets. The stuff above wasnít the only reason, but it was a major part of the puzzle.
Anyway, I think youíre technically in your rights to make your son show you whatís on his phone when heís with you, but I wouldnít do it, at least not by forcing him. If youíre worried about some of the games heís playing, ask him what his favorites are, download them onto your own phone, and see if you can play them together. That will give you something to bond over, and you can also judge from your own experience how potentially harmful or not the games are relative to how fun they are. If youíre worried heís on the phone too much while heís with you, try to do more things to keep him interested, but also set aside some time for him to use the phone. Maybe say something like ďItís hard not seeing you every day, so itíd would be nice if youíre on the phone a bit less this weekend. Iíll try to make sure to stay off mine as well.Ē But make a couple 30-minute blocks on the weekend when thatís what heís doing if he wants. If youíre worried about social media, I understand, and he shouldnít be on it at that age, but youíre not going to save him from it by forcing him to show you whatís there. Itís best just to try to make sure you have a good relationship so he feels comfortable telling you about anything there that you really should know about, so you can help him navigate it before he gets to the age where heís just not going to tell you because heís a full on teenager. Maybe you can sign up for his preferred social media and follow/friend him so you can, again, see what heís seeing, but I wouldnít force that one if he objects. But heís 11 ó if you show genuine interest, heíll probably let you in. If you let him get the feeling that you donít trust him and are spying on him, he wonít, and you should stop at the boundary heís set rather than try to break through it.
The way youíve described things sound so much like what my father would do in 2023. So again, it depends what relationship you want with him.