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I think that allowing him to make those decisions is a great step towards independence and shows you value his wishes even though it means you get less time with him. As long as both homes are safe he should feel that he is able to come and go as he wishes to either ( so long as he's not using it as a bargaining/minipulation tool Sounds like you've both done a great job at co parenting even if it hasn't always been easy. Well done!
At 12 my son who adores me started spending more time with his dad and my daughter who adores her father wanted to hang out with me more. As they go through puberty they look for role models of their gender. It doesn’t have to be the dad a male role model like a sports coach, teacher, uncle or family friend. Your son is growing into a man this is normal.
I wouldn’t let him. Work more on your relationship with him. Get organised, meal plan, slow cooker put on in the morning, spend a weekend getting everything in your home in its own place , buy more uniforms to wash less often and get in a strict rountine with the kids if you are not already , have the younger ones in bed and have one on one with your 12 year old after. Play some uno, lay on the trampoline looking at stars or watch a series together.
It’s hard as a single parent juggling stuff , sometimes you get caught up in running the house and forget about hanging out with the kids.
At 12 he would be hitting puberty too, at dads he would no doubt get more one on one if he’s got a partner to help around the house. If he doesn’t have younger siblings to help care for that’s a bonus for him too, try not to rely on him to help out often, he needs time to be a kid. Yeah 12 year old need chores not responsibliltys. It’s hard work for them, I was relied on far too much as a child with younger siblings, I am still resentful for it now. I never got help with homework, often didn’t even get it done.
It could be as simple as dad has wifi and you don’t or he gets to eat different stuff at dads.... talk to him more about why.
It will no doubt strain your relationship and distance you if you do.
If it were a GIRL 50-50 saying she wanted more time with her MUM what would we be saying? Yes, of course, something must be up, she's starting puberty so she might be feeling uneasy around her dad at this awkward phase...SO, if a boy wants more quality time with his DAD, why not? Doesn't mean you can't meal prep, get your shit sorted and do all the things that posters have suggested below. Compromise with 1 extra day but make it clear you are compromising but won't be manipulated e.g. 1 extra day turns into asking for 2 extra days etc. etc. get something written up.
Let him. How hard is 50/50 on kids, I think from his age he should be able to decide where to spend his time at.