I have been in a similar situation this past year.
Fled - he got arrested. We weren't allowed to return home (safeguarding) and didn't want to due to trauma regarding the abuse sustained in the property. He was remanded. We sofa surfed and then eventually came to a relatives' house to await housing. It was a nightmare as I was trying to deal with the police, DV services, Social Care, housing and other organisations all at the same time.
My child just started reception. I had to change schools for them as we can't go to the one they were supposed to go to. It has been so stressful trying to get a new school place and sort out uniform at last minute.
But... it is 100% worth all that. My child is safe. I am safe. No more physical violence. We are free and no longer locked up in the home/specific rooms never knowing when we'd be allowed out and being told what to do all the time. We can do what we want and eat what we want - within reason. It's priceless!
We have just heard about an offer of housing. We should be settled in our new home by half term. It means another change of schools, sorting out another lot of uniform and filling in copious more forms, being quite far away from friends and having to try to furnish an entire house from scratch. But... we shall be free in our own space and can start to recover.
You can do this too. Your child and you deserve to feel safe and happy. It takes time. You have to just try to roll with it. Although it is really upsetting and demoralising at times, the short term discomfort will be worth the long term freedom and safety.