I'm so sorry for both of you, we can deal with grief in fucked up ways, for example emotionally taking it out on those we love and pushing them away, lashing out physically (I've seen family members get into fist fights at funerals). You walked in on her physically cheating though which it way way more difficult to comprehend. You'll know if you've ever grieved how numb that can make you feel and how unhappy she must be right now, doing something like this is completely out of character, she's grieving in the worst possible way.

I'll probably get down voted, and I never ever justify cheating, I think it's such a lowlife thing to do... But I don't think she did this for selfish reasons or to hurt you, I think this is a form of abusing herself, being vunerable and making the worst decision she could make right now because she's at a real low point. I don't think you should forgive her outright, personally I'd try and support her from a distance, I would sit her down and tell her she's not forgiven and you're not willing to brush this aside, but you know she's got bigger problems she's going through right now. I'd be very insistent on boundaries and space until you can both deal with this better, so if she can stay with family or friends who can support her better perhaps? Do not have sex with her, she needs to also be tested for STIs. I would attend the funeral if you are close to her family, let her cry on your shoulder. After the funeral, once things have cooled off, that's when you need to make a decision to either break things off altogether, or put this aside as a one time mistake, and try and make the relationship work, even then it's going to be tough and couples counselling could help.