Hi there
You are in a bad place with all this, and family and friends reactions are not helping. I, too, think alcohol played a big part, as well as the heightened emotions after the argument with your sister in law. We all do things we regret, things we are ashamed of. I think this is between you and your partner. Nothing else matters at this point. Couples can and do recover from infidelity. Concentrate on the two of you first, then you can face the rest.
Sometimes we just don't know why we do things. We aren't always rational, and don't always understand the complex workings of our own minds.
The people we hurt want a reason, they want to understand it, because this helps them cope, and recover. If they know why, they can make a judgement about whether they think it will happen again.
Do you think couple's counselling would help?
Hugs