Some real advice from a fellow father ...
I'm 36 and I've been playing since 2004, and my wife has always been relatively supportive of my disc golf obsession. She knows that this is one of the ways I satisfy my need to be outside, to be social with a diverse group of friends, and quell some competitiveness that would otherwise manifest itself in games of scrabble played for blood. We've been married since 2007 and have two kids (a 4-year old boy and a 9-month old girl), which has significantly reduced the number of casual rounds and tournaments I get to go to.
But she's never told me not to play, I've just compromised and accepted that with two small kids, my time is more valuable at home or out with my family. To counter-balance the Sunday league round, I do a TON of work around the house on Saturdays and early Sunday mornings. I do all of the laundry, sweeping, vacuuming, and general cleaning I can. I'm the one who gets up early with the kids at 6am so she can get some extra sleep. In return, I stay home on Sunday afternoons with both kids so she can go out and get some time alone for herself.
We try to make Saturdays our family day (go to the movies, run errands together, etc), and make Sundays our day to be adults.
If you truly love disc golf, she'll understand that, and if she doesn't, you should sit down with her and explain why you love it. Make the time for her that she needs, make the time for your kids that they need, and she'll understand that you need time for yourself. And if she truly thinks disc golf isn't exercise and that's why she doesn't want you to play, show her a bunch of videos of top pros crushing discs, and then have her try to say why disc golf isn't athletic.