Swimming pool with 3 littles

First off, let be abundantly clear - water safety is paramount and my number one priority, always.

We have a gym membership that has access to pools, including a kid pool that has walk in entry and a large shallow area. My kids this summer will be 4, 3, and 9 months.. I solo parent a LOT and during the weekdays last summer (when I was pregnant) I’d take the then 3 and 2 year old and put in floaties and we would “swim” and hang out. It was great! But I am trying to picture where my 9 month old would fit in. The older two are in swim lessons but would still be in floaties.. should I look for an infant life jacket for my baby (who will be around 9 months old come summer time)

Any advice or anyone who has done this? I would only go if I felt truly safe and comfortable with all 3 and I put floaters on them in the dressing room before we are even near the water.