I personaly wouldn't give a crap what my neighbor said about my yard, it's my yard. We have a couple a little younger than us living right next door and I swear the guy is OCD. My husband mowed the little front part of our lawn when we first moved in and they have a bush and some flowers with mulch in their front. That guy was out there on his hands and kness picking the few tiny pieces of grass that landed in his mulch

.
I seriously don't know what I would do if I had a neighbor like you do, I'd probably have a nice talk with her

. Especially since you're so nice to her son, she should appreciate you.
As far as the grass clippings (we just let them lay but if the grass was high and there's alot, we rake it up, put it in a garbage bag and dump out the bag in the woods across the street). Have you thought of maybe investing a mulching mower? It mulchs up the grass really finely as you mow, so there's practically no clippings, good for the lawn too