"Stresses at home" is highly euphemistic in the circumstances but I'm glad you're taking active steps to leave. That must have taken a great deal of strength and courage.
Have you spoken to Women's Aid? They have a webchat facility.
Personally I think that would be a very sensible first step. Your eldest is too old to join you in a refuge but they can talk through your other options and look at whether you may be able to access other support.
Entitledto is a good shout from pp. Work out how much you would receive in UC. Money advice service can help with budgeting and knowing how to navigate practical stuff.
Citizens Advice can be really helpful about finances, DV, housing, divorcing etc.
Knowledge is power, so gather up information and start building yourself a plan.
If your current job is very part time then you might be able to find another job that fits alongside to top things up until you can find a job that's more hours.
Have you looked at rental properties available right now near you?
You don't need a forever home or super long term plan, you just need a stepping stone to start the process of making the changes you need.
Good luck.