A good way around the food thing would be to keep a small dish of green beans (fresh or frozen, canned are too salty!) or diced carrots to give as treats, instead of the many things that they shouldn't have. The begging thing is annoying and not adorable, but you could at least make sure that what she's getting is not going to make her heavier or sick.
It took a long time for me to convince my husband not to feed our Starr (RIP) at the table
I had to put it to him in terms of money (expensive vet bills) and death. By that time she was a seasoned beggar and would jump high up in the air and bark sharply at the table. NOT cute!
Good luck with this, I hope you can get him to stop!