How can i Get the one i love to trust me again?

I need some help, I’ve recently split up with my Ex partner of 3 years, We have 2 kids both 1 Year old and I really do want to be able to change what I’ve done and Prove to her I’m not the man I used to be.
In the past I HAVE been un-faithful (Not sexually, but just Verbally ie. over emails and such) but I now know what I’ve done wrong and what I must do to ensure nothing like that ever happens again. Also I was Heavy cannabis Smoker for 12 years which got in the way of showing the ‘real’ me and in a way it just made me lazier and less caring and sometimes a little bit angry ..but since the break up I’ve managed to Stop smoking it, Seen Councellers for my behavior had quite a lot of sessions and used a lot of techniques to learn to take control of myself and ensure I can be the best man I could dream of being and its worked.
Recently we have been seeing each other as friends and doing ‘family activities’ which has really made me think about our future, The one thing I’ll ever want is to give my ALL to her and my kids with nothing or no one stepping in the way. The past few weeks I’ve been asking her where we stand and showing her the changes I’ve made in life but she keeps saying to go with the flow.. She has noticed the changes I’ve made for her and the kids but she keeps saying I should change for the kids,.. but in fairness I want to change for the family, I want to be the loving Father and I want her to be proud to call me her man.
Obviously she’s lacking trust in me and chooses not to believe a word I say and I really don’t know how I can show her that I won’t be making the same mistakes again and I want her to believe in the changes I’ve made,. I HAVE done everything I can to change to be a better man, changes that no one would ever imagine me making but I’ve done it.
I Tried talking about the future with her last night and I wish I didn’t now. She told me she can never trust me again, I asked her if she loves me she didn’t say no, I asked her if she thinks we’ll ever get back together she said she doesn’t know. When I’m with her I can see the love in her eyes, and she treats me like she would if we were still a couple, but there’s always something missing, she hugs me, but doesn’t kiss me, if I mention the future she changes the subject, She tells me that she wants to be able to see if she can trust me again (obviously I know it takes time to rebuild trust) but I don’t know how I can let her see that I am trustworthy and a better man. if I ask her what we should do ie.. Should I move on.. she goes quiet and says ‘dunno just go with the flow and see what happens’ (meaning with me and her) which to me makes me believe I should wait for her to trust me again, the last thing I want is to move on or find someone else, I Love her and only her but I don’t think she see’s this. I wish there was something I could do to Heal the wounds and Bring our family back together again. I Broke her trust but I want her to see the changes I’ve made and learn to love me again.