As a parent educator, I would look at her and tell her that this is Mom's pocketbook. Put it in a closet where she can't get to it.
If she does try to open it, you must change your tone of voice and tell her that this is Mom's purse and she cannot have it. Period. Move it out of sight. If she tantrums, that is ok because that is how a child learns and grows socially and emotionally -- and it's discipline.
OR
Put an old, empty pocketbook out w/ safe items inside and leave that out !
It is not too early to discipline a 2 yr old. "Discipline" means to teach. You are simply teaching her that it is not ok to go inside a purse w/ credit cards, etc. Yes, she is curious at 2.
So, give her another grownup pocketbk w/ a few old cards, etc... (as I mentioned). She probably won't want it!
Or tell her no and a quick explanation why. It's about having a plan and sticking to it.
My 2 yr old used to open all the drawers and take everything out ! Tons of stuff got pulled out ! I put child safety locks on all but 3 of the drawers w/ plastic bowls, cups and lids. She pulled on the locked drawers and cried for a few days. Then, she realized this is what was going to take place from now on. I made a plan and stuck to it. Plus, I didn't have to clean up constantly !!!
I always tell parents that this is good practice for what is to come w/ girls.