Four weeks of silent treatment is four weeks of emotional abuse from him towards you. This relationship is over anyway because of the level of abuse he metes out towards you (and in turn your kids who will indeed pick up on all this). They are also receiving very mixed messages; he is being overtly nice to them whilst otherwise ignoring you as their mother. This dynamic, if you choose to remain in it, will further just mess your kids up and they could repeat similar in their own adult relationships.
What do you want to teach your children about relationships and what are they learning here?.
What is so bloody fearful about being on your own?. Feel the fear and do it anyway; it will likely be the making of you. You would not be on your own anyway because you have two children also to consider here. You're not being spoken to at all now by him; do you not feel alone within this relationship?. Feeling like you do is akin to a slow death by 1000 cuts. Better to be without this man than to be as badly accompanied as you are now.
Re your comment:-
"Everyone I speak to me tells me that all long term couples go through things like this."
No they really do not. Abusive relationships are like this, not emotionally healthy and respectful ones. No-one's seemingly ever bothered to show you what one of those is like and you still do not know (this is not it). If your friends are saying this crap to you, you need to drop them like a hot brick because they are holding you back and stopping you from reaching your full potential. They do not have your interests at all at heart here. You are absolutely entitled to a life whereby you and in turn your kids are not on the receiving end of abuse.
This man does not want change; he seems quite happy as he is because you're also doing the cooking and cleaning for him. He will be happy to continue in that vein too.
Honestly better to be apart and happier than to be together and as miserable as you are now. Do not get bogged down in your sunk costs. There are two ways to understand this process, both involving avoidance. One is an avoidance of disappointment or loss when something doesn’t work out. When a relationship doesn’t succeed, especially after a long period, especially after many shared experiences and especially after developing a hope that the relationship would be a good one, it is a loss. It is a loss of what might have been and an acknowledgement that a part of one’s life has been devoted to this endeavor.
Another angle to evaluate is that focus on “sunk cost” creates a distraction from one’s inner truth. The sentence often goes like, “I’ve already invested to much, so I can’t notice my thoughts and feelings that are telling me to end or change this relationship.”
This is a type of insidious defense against noticing yourself. You enter into a neglectful relationship with yourself which divorces you from your inner thoughts and the quiet feelings that might guide you in your life. In other words, thinking about what already has been may prevent you from deciding what you want your life to be.
After this weekend Christmas will be over; what then for you and this person?. Make the break and make 2022 a potentially far happier one. Your children will also thank you for doing that.