I think you'd be surprised about the moms at your pool. I doubt they're wearing bikinis only to "show off" their bodies. In my case, it's comfort all the way. I look like a dork in a one-piece and feel claustrophobic when I wear them. Either it fits my hips and is too loose on top, or fits my bust and tight as hell on my hips! I'm just disproportionately built. I also hate the feeling of wet swimsuit sticking to my belly (don't ask me, I have some kind of tactile sensitivity). I find bikinis are way more comfy and athletic. They're just swimsuits, in my opinion Why would I want to wear one at a kid's swim lesson? To avoid having to purchase a one-piece for the occasion. Simple.
(I wore a bikini when 6 months pregnant in Hawaii and no one looked at me twice! Saved me from having to invest in maternity swimwear!)