I think a letter to the top brass is in order. I volunteer with TWO groups that have 2 separate Petsmart adoption centers. #1 has very few restrictions. AM and PM cleaning and they can do adoption days any time they like. #2 wants more participation on the part of the rescue group (but nothing like you are speaking of). It is AM and PM cleaning and at least 1 shift sometime during the day to exercise cats and great people. The more time a volunteer is there the better, but no exact demands. Both Petsmarts do allow other rescues to come in as per their schedule to do adoption day events.

I too think they want to force you to leave in order to bring in another group. I would not give up without a fight!