It is a long process. You have to show her consistently, every day that you are being honest and open with her.
How do YOU know this? You are feeling very sorry and afraid right now because you don't want to lose your wife, but what tools are you putting into place to ensure this won't happen? Most people don't plan to cheat, and then they do.
How do i prove i wont strey or cheat ever again an truely want only her rest my life?
So, before you start trying to 'convince' your wife that you will be loyal and true the rest of your life (which is what you have already promised when you got married), what are you doing to actually make it happen?
This is what she needs to see you doing. Working on YOU, being true every day with actions standing by your words. No boundary crossing, no lying, true focus on the M and fixing yourself, every single day.