It is made even harder when your child/children, are holding on to their dream family of mum, dad and them being together. This has resulted in many spouses staying with an A, sometimes in an abusive marriage, "for the sake of the kids", when those kids did not know how awful it was for the sober parent.
Honey, you are the one who is in this situation, who is the adult and needs make decisions based on what is best for you and your child, while your child may feel you are in the wrong. You are not choosing to end your marriage and walk away, out of some whim or for fun, but because your partner's addiction to drinking is unbearable or unsafe.
My daughters were in their 20's when I left their father, and it came as a real shock to them and others, at the time. My eldest even ceased speaking to me, as he convinced her that I was "going thru change of life hassles", and playing round.
It didn't take them long to find out why I had left. After he'd moved in with the first 2 for less than 6 months each, they couldn't take his demented talk and messy habits and he ended up with eldest, who lowered the boom on him and took some control over his medical and financial affairs.
You can only do what you feel is necessary for improving your lives, and care for yourself and your sanity, til eventually your child realises that you did your best for them, and at some stage they will get the message. Til then it will be hard for you, but hang in there, take a look at Alanon and use SR for help and support.