Honestly, sometimes family is the biggest detriment to us - be it the core family, extended family, step family, or family from friendships. Our family has the biggest impact on us .. so if we already feel horrible about ourselves, a simple constructive criticism can feel like someone stomping on us, and a small insult can confirm the feelings we already have.

Your sister in law seems to have issues with her sister being with you. I would gander a guess it's either bc (a) she truly does like you romantically or (b) she is jealous of the relationship. I would recommend ignoring the sister in law n sit your wife down for a talk about how she feels about your relationship n give her assurance her opinion matters to you. Affirm her feelings by listening and asking questions. After she is done- tell her how you feel about the relationship. Good communication will help here, I think. *hugs*