What kind of person am I dealing with here ? What should I do?

So I have been cool off and on with the mother of my child since I cheated on 2017. Since than she met someone. Decided to be with him and moved him in with our 3 year olds of course I was angry at that. One month later moved him out than started to talk to me more and allow me over more things got better but turn for worse everytime she goes back to him tellin me she’s done. I’m in school to get my a&p license with 3 months left and unemployed due to the airline decline. l have took her on free trips and she talks to her ex and expect me not to get upset instead say she can do what she want she single, even though she carry’s on with me like one big happy family and wait to be with me officially until I can provide financial and take over the bills. Recently her car broke down so I stay with her to get the girls to daycare and her to work and I pick them up. Now she’s starting to carry on the phone with the guy morning and night and expect me to think it’s nothing knowing I want to work on being a family. I NEED ADVICE IM 27 SHES 23.