Hello and welcome to SR, Jeep08.
I too, have an AW. I too, distrust her. I also resent her. She's also supposed to attend an outpatient program. We'll see about that.
You asked a question in your first post. "How do I give her that chance and try to trust her again?"
I struggle with this same question and after spending a good amount of time on myself, I have an answer that works for me. My AW won't get her cake and eat it too. I won't give her both a chance and trust. Those are separate topics in my life. She needs to prove to herself that she can get sober. I'll give her that chance. I've set my boundary. If she doesn't find sobriety, I will divorce her and she knows this. So now is her chance and it's one that I'm giving her. Does that make me controlling of her? No. I maintain the control on myself. She'll do whatever she needs to do but at least I'm not filing paperwork right now. I won't control her or monitor her anymore.
Trusting her again will happen once she's able to prove via action that she's working her plan and is sober. She needs to do the work to rebuild that trust. I've decided I won't be such a codie and grant her trust because she puts forth some token gesture. I take a hard cruel stance on this. I don't pipe off hard and cruel towards her. She does it to me. So again, just like they have to find sobriety for themselves, they also need to prove they can be trusted. Weather or not I see it, is up to me.
I don't know if that makes sense but I hope it helps. Sometimes I've found myself trying to eat the whole elephant when I really need to take one bite at a time.
Good luck man. It's a tough ride. I'm very proud of you for taking care of you and your kids. Keep on posting and writing. We get it.