Dont admit to any fault in email. Dont say "I know I had issues..." or "Im trying to be better...". You WILL lose custody if you give her free ammo like that. She looks like she is running circles around you.
When she directly or indirectly blames your drinking you either dont respond, or you factually refute them at least 24 hours later. What you are doing is trying to diffuse conflict by admitting some guilt while trying to even the score with some sort of veiled accusations about conflict. It is extremely passive aggressive, makes you look guilty and and makes her case look stronger. Also your condescending attitude is not winning any points with her, I can assure you.
I suggest you ignore the vast majority of these emails from her. If there is one with particularly bad false accusations you respond ONLY to the accusation, and you do so sticking to facts, no feelings: "I am not drinking. Jan XX was your parenting time. I will be responsible for caring for D4 during my specified parenting time. I exclusively have been taking care of D4 during my parenting time, and yours on the following dates XX XX XX over the past 2 weeks.
You requested D4 visit your parents partially during my parenting time. In the interest of being cooperative in our scheduling I agreed. I did not relinquish any of my parenting rights or responsibilities. Your accusation that I was unable or unwilling to watch D4 on my parenting time is completely false."
