Thankyou for your honesty) you have lots of insight into your behaviour that has been erratic. You feel however that it is too late to repair the damage.
The real answer to this lies in your wife's decision. There is some things we cannot control and other peoples choices are theirs alone. Some might be convinced of a new leaf turned but they are in the minority. Also, having children involved can sway your normal tendency to move on, an attachment understandable, beware of that. Children are resilient and adapt far better that we do. A school principle told me that after I kept ringing every morning to see how my daughters were coping. "Better than their father" she blurted out.
I made an attempt on my life. It was 1996 and the emotional abuse over 11 years was too much to bare. Then like you I thought of my kids (7 and 4yo) and left one week later after a smoke ring was aimed at my face. I left, decided I'd dedicate my life to my daughters to be the best part time dad ever. My eldest came to live with me at 12yo and at 28yo she married and as we approached the alter I asked myself- "who wouldhave taken my place?" It was then my daughter said "thanks for hanging around in my life dad" Tears flowed- I made it.
I can only offer you my ideas. I would pursue medication more thoroughly so maximum stability is achieved, therapy - whatever it takes. Learning on this forum is good for between visits to the psych for education.there is thousands of threads here just use search.
You would know better than anyone if your wife needs space, time to trust or is missing you. As my therapist reminded me once- "action speaks louder than words." You cant betray your word that you've changed- it doesnt happen that quickly even with the right meds and this is the outlook your wife likely holds. Some of our behaviours is mental others is personality. So, I'd meet with her at a cafe, be frank and regretful. Tell her what you have said here and leave it to her to choose. Talk too much and she'll turn away. Lighten up the latter half of the meeting with laughter and talk of the children. When you depart, inform her that you wont pressurize her. I'd then allow what I'd feel is a reasonable period of time to receive an answer (I would not ring her- thats her job) then I'd move on.
when all is lost what can you do? be radical
Caring for your 'well' partner
The best praise you'll ever get
Anger and frustration