Hi P.!
I'm really confused with this. I have 2 boys in the house, and YES they wanted things they couldn't have when they were 2, but did they get it?......NO! not if they WEREN'T supposed to have it! The gum issue was no different. Most kids want gum, but at 2 it's hard for them NOT to swallow it. My "gum rule" was that they could have it only when they sat at the table and colored. I didn't want gum everywhere, especially in the carpet (like the fruit snacks ended up), so they had to sit at the table, and that was their only opportunity to have it. I only bought bubblegum Trident or Extra, and they could chew it after a meal (as to help clean their teeth). If they swallowed it, then the next time they wanted it, I would say "I don't know, honey, last time you made it go to your tummy, and that's breaking the rule, if I give it to you, you cannot swallow it". After a few more tries, then the problem was solved, but only in my sight, and only at the table. My youngest is 5, and still has "gum rules" and "cough drop rules" and "hard candy rules", mostly for choking reasons.
As far as going into your purse, I ask "why is your purse low enough for him to get into it??". Especially when you're having this problem. That's mommy's!!! He needs to learn NOW what is NOT his needs to be asked for. Otherwise, he'll begin taking ALOT of things that aren't his. Just give him the words to use "honey, this is not yours, you need to say 'Mommy, can I have some gum please'..." If YOU are the one that is negligent (by leaving things accessible), then he should only be told that it wasn't his and he forgot to ask. Don't make it about the gum, make it about him taking things that are not HIS.
I think you need to "re-vamp" your home for a 2yr old busy-butt! This is just the beginning :o)
:O) N.