I agree that we can't work on our relationship as long as she is working on another one.
You're spot on here. It's impossible to recover the marriage while she's pursuing other people. I worry that she may need to be shown what she stands to lose to snap her out of it. She seems to feel you'll be there either way. She can come home now or she can play around for a while, sow some wild oats, and then come back to you. You have to decide if you're ok with that. If not then go ahead and file. A lot of people think that is not good but filing doesn't mean it's going to happen and a lot of times it snaps a wayward spouse out of their fog. Show her how wonderful of a choice you and your/her family is. Far better than dating especially considering she's using Tinder. Only creeps out there.