Sausageroll123 sorry you're going through this, it's really shit - I've been on the receiving end of it too.
Growing up, my dad always did this to my mum and she would grovel and he would eventually deign to talk to her again. It was horrible, we would walk around on eggshells until the next time. It was always when my mum would voice her annoyance or what have you. He would never apologise, you couldn't criticise him or anything.
I ended up in a similar relationship, except my ex would take anything that had gone on out on me. We could be in the house, separate rooms and he would suddenly stop talking to me - even though I hadn't said anything to him!. If I asked him for help, he would grunt or what have you. If we had an argument and he didn't like what was being said he would walk away and ignore me.
If we had plans for a weekend, he would ruin that by suddenly being a dick and ignoring me or ordering me about. There were a few times he would tell me it wasn't working out between us and end the relationship. It was bloody awful.
The day after I had an operation (and had to be admitted) he wouldn't help me sort out the bedroom and I had to climb over things and risk further injury...to this day I have no idea why! He literally went to bed, told me no when I asked for help and said that I should go away (the implied threat being I need to leave otherwise he'll lash out).
After. Every. Single. Time. he would apologise, he's sorry, he didn't mean it, he's stressed. The reality is (and this came out in couples counselling) he was insecure and rather than deal with his insecurities all of these times he said the relationship wasn't working or went silent, he was testing me. To see if I still loved him and if I grovelled and say "no, I want us to be together" or whatever it was (honestly, similar to what you have been saying here) "proof" that he was worthy or some shit like that. He did it to get that reaction of grovelling! I wouldn't be surprised if he thrived on it.
I also wouldn't be surprised if he truly believed I loved him more than he loved me.
One time (quite frankly the beginning of the end), after my birthday, after ignoring me the whole time we were at a bar by playing on his phone (and demanding/badgering me to get his other phone!), then shouting at me because he left his phone in the hotel...(bear in mind NOTHING had happened in the day to set/piss him off) he tells me this isn't working and reels of a litany of reasons why. I felt the familiar pit in my stomach - I had given up too much for this man, I can't let go now. And then I stopped, and got angry...so I agreed with him. I told him he's right, gave my own reasons why we should break up.
You want to know his response? "Aren't you going to fight for us"? I asked him why would I do that when he's just said he doesn't want us to be together?! He had no answer. The next day he cried, he apologised, he didn't mean it, he loves me etc. etc. The cycle of abuse (in various ways, not just the silent treatment) continued for another year and half before I finally had had enough and told him I wanted a divorce (yup, stupidly I married him!). This is just the tip of the iceberg - he's ruined various events and days out for me with this silence.
What he is doing IS abuse - it is emotional abuse, it doesn't have to be physical violence for it to be abuse. He is fucking with your head and trying to control you with silence. This guy doesn't like what you have to say, he doesn't like you being upset and not loving him unconditionally. So to stop you, to make you feel bad he is punishing you with silence.
Do not be fooled into thinking that it is him just being stubborn or whatever, he is punishing you. If he was an adult, he would tell you WHY he isn't talking to you and to ask for space. He would communicate that much at least. He doesn't do that because he wants to to spiral like this, to grovel, to cajole him back. It makes him feel powerful and wanted. It is fucked up and you deserve much better.
Your kids deserve much better.