I think you need to consider what will happen in a couple of years time.
Your child is already 4, they are heading for full time school & it's only a few years before you don't need childcare any longer.
That makes a big difference to your budget & to what you can do workwise.
If you leave this council house, will you ever get back into social housing if you couldn't stay at your mums any longer, or would you have to go into private rentals (higher costs, less security)?
Will you really be okay living with her long term & would she be okay with it too?
Going back to live in your parents house is not the same once you have learned to live as the adult/boss of your own home.
This would be her home you get to live in, so it would be her rules not yours.
Are you better placed for work where you live now or where your mother lives?
How about schools & childcare in both areas?
What about your friends?
Do you have a support network where you are now that you will lose if you move?
Do you have people other than your mum where she lives?
Do you want to date at some time in the future?
Do you feel you could do that living with your mum?
Mostly, it depends on how good a relationship you have with your mother.
If it might go wrong, you will be in a much worse position than you are now.
If you have a bit of a bumpy relationship, I wouldn't risk it.