Make AP come to an indoor public pool now. Let them know you want to see their swimming ability as well as being able to handle the kids with you and lifeguards available.
If AP can indeed swim (I've heard ridiculous claims that they can "swim" if their feet can touch the bottom) AND are attentive, then go over some pool rules like NEVER leaving them unattended, 0 phone use or sitting outside of the pool while kids are in, being x number of feet from each child at all times, requiring life vests on at all times, and NO pool "play dates."
Also, if you have more than 2 non swimmers, then it's a hard no. An AP has 2 hands/arms to hold up 2 kids.
If AP does not pass, then I hope you have a safety cover (one of the ones that can support a 500lb person falling on the cover and it doesn't fall in). Go over "house rules" like not trying to take it off and that you will be keeping it closed all summer, so don't try to invite friends over for a pool party when you're not home for a weekend. Buy an inflatable kiddie pool for splashing around instead.
In addition, I'd be taking a hard look at whether I really like AP and consider rematch. We used to have a outdoor in ground pool at our last house and emphasized we NEEDED a strong swimmer for our then nonswimming kids (1.5, 3.5). The older one was close to being able to swim, but not reliably enough that I would allow AP to be a nonswimmer. The deep end was definitely too deep for any adult's feet to touch the bottom. If that AP had turned out to be a nonswimmer, I'd still be feeling incredibly betrayed by the lie and HUGE safety hazard of using our backyard space. Yes, the pool was fully fenced in according to legal standards, but not separately from the backyard.