We were in Montechoro from 30 Jul to 13 August, and I too noticed a glut of beggars (perhaps not the right word to use for a collective of beggars..!!!!!!) but they didn't hassle us for money, just sat on the pavement.
There were also a lot of blokes with glo-sticks and yapping dogs trying to target the kids, but with a quick shake of the head they were gone.
We didn't really find any bars which specifically had things going on for kids, but ours were happy watching the "funny man" mime artist at the bottom of the strip.
I agree though, that the Old Town knocks spots off the Strip for atmosphere and ambience. We caught the train down every other night for something to eat, and then would wander up that little alley to watch Mario Miguel (tonight Matthew, I'm going to be...Neil Diamond!)
Slightly disappointed that Brian Cristopher wasn't in residence at Sir Harry's Bar as he had been ten years ago on our last visit - but the chap that was there was very good indeed (can't remember his name - anyone help?). However, he didn't start until 10.30 and our kids are 7 and 3 so it was a bit late for us, by the time we'd got the train back to Montechoro.
I think, and always have thought, that a holiday is what you make of it. You're going to see or experience things that aren't quite what you'd like, but hey... you'll get that in any resort in any country. It's how you deal with it that makes or breaks your holiday.