[DamSweet]

I have read several threads on this and am still confused. I am afraid that Bridget is becoming aggressive. What confuses me is that she is not aggressive with her food (mostly because there isn't a food that she loves). It happens when she has a toy (usually a chewy toy) or a treat such as a bully stick. When you approach the item she stiffens up, stops what she is doing for just a split second and whips her head around toward you and snaps and lets out a yap. Yesterday she had a little ice cream from my spoon and some dripped on the floor, when I went to pick it up before it melted - she snapped. Almost no warning (no pre-growl or anything) - it's not like when she has a toy that she wants to play with.....she has a playful nip - actually never bites down. She has a huge supply of both toys and treats and is free fed. So she can't be worried about not getting more, and like I mentioned earlier....it's not with her food.
She will go right over and push my cats away from their food dishes, but heaven help them if they want to check hers out...or their own for that matter. But normally not as aggressive with them as with me, maybe because they just back off.
Bridget is a little over 6 months old and I have read in threads that a pup that young does not normally exhibit aggression. So - if it's not aggression - what is it, and how do I stop it either way. I have 2 grandchildren, 1 of which is only 9 months old, but the other is 5 and has been taught not to go near a dog that has something that it is chewing or eating, but children forget and I would just like to be comfortable taking things from her in the event she gets something she shouldn't have, such as when a bully stick gets too short.
Do I distract her with something else first? Do I scold her when she snaps? Or is this just normal Yorkie behavior? I don't want to make matters worse so I'm coming to the place where I know someone can help.

Thanks everyone for listening - any and all suggestions or thoughts are very welcome and appreciated.