Would you take a woman back for emotional cheating and going on a date with a guy?

I've cheated once emotionally once with her ( I use to get girls number just to make sure "i still had it" but never texted them more than an initial texts and never went on dates with them.)

She cheated emotionally months down the line. Told me she was going somewhere for an event and ended up going there with someone ( on a date )

And then she lied to me recently about going to a business meeting. We had been getting in a lot of arguments before this ( so anyway guess she left early from this business meeting to go hang out with her ex) she did confess..... and she said it wasn't for the reason I was thinking, but to ask him about his opinion about being accused of cheating ( I accused her of cheating before this indirectly and she use to accuse her ex of cheating so I guess she was trying to put herself in his position) I found out about this through a friend she said she was with turns out she was never with her. ( This was all within a year span btw)

I broke it off with her and told her it was because if her disrespect dishonestly and if I didn't respect myself enough to leave that she would not respect me. We life together at her moms place. Anyway I left. She was bursting out in tears and asked me what I wanted and if this was a see you later or a see you never again. Told her I'm wasn't really sure but I was sure I neede to get my stuff together and we need to not see each other for a a day or two, maybe a week or even a month. She blew up my phone the same day with text messages about how she misses me. I'm now at my parents house.

It's the next day and I know she will end up texting me eventually, ( she did actually about something logistic ) plus I need to get the rest of my stuff. Only god and her knows if she was physical with them.. If you really loved her and saw yourself being with her would you take her back? Or is this really unforgivable?