Yeah this didn't flow and was a little disjointed, both in text with all the commas as well as in reading it aloud.

The joke is weak but salvageable to bridge material, IMO, at least for a quick, unexpected laugh. I'm no comedian but I'll try to rephrase:

"A lot of us in life have dealt with that one annoying rich kid, you know the one, who would have bragged about the size of his pool. Meanwhile being poorer kept me humble... I mean, after the water at my house was shut off for a few days, you didn't see me bragging about the size of the shit I took in that pool, did ya?"

I dunno, I'm quite drunk but that's the rewrite I'd find funnier.