In regards to taking time away from the kids, I would judge her resistance no more than typical when compared to other mums in similar situations. She sees it as a chance for father-child bonding time, so she does not feel any guilt from being away from the kids.
Have you found a way to balance family life against hobby life against work life for you and family? I am still searching.
That's great! So if you take more time solo w kids then she will get recharged away from them and get more friend or solo time. That opens you up for the same.
I do that to give me balance and help my wife out. I'll take a full Sat or Sunday with the kids. Then I just make sure to express in advance that I want to golf/kayak/fish/bowl/etc and she's very understanding now.
Golf and fishing are easier to balance because I can do them really early in the morning. So if I can make that work I do it. Then you can nap w the kids later. :)
I also hit the driving range on my lunch break which is nice. Or do a short par 9 during work time.
Actively encouraging your wife to do solo or friend time will open your game up. :)
And then just fitting it in when you can haha. Worth sacrificing some work output when you need it IMO, but I run a small company so I have some flexibility others may not
Have you found a way to balance family life against hobby life against work life for you and family? I am still searching.