My twin girls are 18 almost 19 months old and I have been seeing this a lot lately. One of them starts playing with something and the other one wants it. They've hit, bitten, and knocked each other over!
I do think that it would be very typical for you to see some behavior changes when changes to their daily rountines happen (change in caregivers). Some of it too, I think, is just typical behavior for their age.
They don't really know how to share yet, they can't verbalize their wants or frustrations very well. You just have to decide how you want to handle the situation. For now, I have pretty much been redirecting or removing them both from the situation.
Hang in there!
Dana, mom to Avery & Natalie 7 , Cole 4 , and Baby #4 on the way!