OP I don’t like to be harsh but have to echo a lot of what’s been said here.
You don’t seem to be taking responsibility for this massive mess.
The way you speak about your wife is shocking. She is a person and your utter contempt for her is clear in every posting.
Alcoholism is a disease and she would need support and strength to tackle this. It seems like you are blaming her for her addiciton. I also note her parents were alcoholics too so she’s not exactly had the easiest start clearly.
You seem to thinking marrying her was a huge favour to her but YOU choose to do this. You chose to trap her in a marriage where her husband clearly sees her as worthless. You then decided bringing two more children into this toxic mess was a good idea.
I genuinely can’t fathom your reasoning here although from the style of your posts I am sure you will say the children were due to her lying about contraception or something similar.
You call her a bad mother so I am assuming you took the career break and did all the nappies and have been solely responsible for childcare? If not maybe cut her some slack here. No ones perfect but she is a person and you speak about her as if she is a misbehaving pet that you don’t want.
I’m not saying any of this to say stay in your marriage by the way. If you are unhappy for both of your sakes you need to split.
As for your son again I think you and your wife need to think long and hard about being honest. If he finds out the paternity doubts from someone else I’m sure it would be devastating for him.
I hope you resolve this in a sensitive manner. I do wish you luck OP and of course you deserve to be happy.