Kids can drown in a wading pool, tub, or inflatable pool. Two feet is plenty!
Never leave kids unattended near water.
https://kidshealth.org/en/parents/water-safety.html
All that said, it sounds like fun to me. I don't have a perfect body but love swimming and water and I'd go and be in the pool with my kid, without a care about my cellulite and post-pregnancy rolls. I'd go to a park or anything outdoorsy just as enthusiastically. At most of these places, you do have to buy and bring your own cake and food. I don't know of an adventure type outfit that takes care of everything. If someone does, I'd also like to hear about it!