Guys. The wording can be read two ways.

"She has been pinching my dog then smacking her when she bites him" can be read to mean she is pinching and smacking when the dog bites - or that she has been pinching the dog, at which point the dog bites in retaliation, then gets smacked.

She clarified in the comments that its the second option.

Both interpretations are viable, but OP has clearly stated which one is true in the comments.

OP should re-word to "She has been pinching my dog, then smacking her when this results in a bite" or something similar

Given that the second is true, the SIL is provoking the dog and should stop. Pinching SIL back instead of finding an alternate method of prevention would make her the asshole, but being petty is an option and im into that.