Sorry, Bubba, siding with your wife on this one.

1) Between the ages of 0 and 3 there are plenty of daycares who will take your kid on (for increasing pay). Between 3 and 8 there's a total black hole where there's fuckall your kid can do unless you start looking for camps in - wait for it - January. About age 9 or so things open up a bit and you have more availability but the stuff that isn't prison camp fills up fast.

2) The whole point is to get your kid in an enriching environment where you don't have to entertain them. What do you plan to do with your kid all summer? 'cuz they're young. They're either going to be up in your business every waking minute because they're social? Or you're going to plop them in front of an iPad.

3) League sports are good for an hour a day tops. What are you going to do with the other 9? My daughter swims competitively which basically means an hour and a half hole in my day four days a week. That's not a summer, not for you and not for your kid. Besides which you can't really do fuckall until like 6 or 7. Even the serious camps (my kid did 6 hours a day of rock climbing between 5 and 7) are only good for like 6 hours, and rarely for more than a week.

4) The good camps are fuckin' rad. My daughter does "cake camp" every year, for like $700, and comes home with about five parties' worth of baked goods. And you know what? She frickin' knows how to bake, and how to decorate stuff, and has helped out the shop at the state fair and stuff. She also does this one called I-Shit-You-Not "Ninja Foxes" where they learn things like how to use a compass, how to whittle, how to track game, how to walk stealthily and how to make a fire with sticks. It kicks the ever-lovin' shit out of boy scouts; no idea bout girl scouts.

5) The good camps expose your kid to materiel you just don't have available. do... you own a potter's wheel? How 'bout a kiln? Are you going to take them hiking every day for a week? How'bout a zip line? My kid spent several weeks during COVID doing slack line, laser tag and axe throwing. she was seven. Now - I would argue that "hyper-supervision" is a positive trait when your seven year old is learning to throw an axe. But she also had several "find your way to the secret location using a compass and orienteering" at the age of eight.

I suspect your head is wedged about this because it's fucking ridiculous that you need to plan out a five year old's schedule six months in advance but your wife has accepted the reality of the situation while you're pissing into the wind. Cut that shit out and recognize that maybe she'd like to do something with her life while the weather is good and exposing the littles to new environments and new friends is really fucking important.