How do you apply for jobs without references?

"I wanted to know what their work ethic was. I wanted to know how they got along with their co-workers. I wanted to know if they were a self-starter? A team player? Trainable? and above all RELIABLE."

Seesaw and Wishful Thinker have both given good examples of professional references. I'm quoting Seesaw because you may also find with well-disposed people that you need to give them some idea of the qualities needed in your new employment. I've written references for myself twice when I had referees who felt kindly towards me but didn't really know me super well, in extremis that is. Give them a script and ask them to type up whatever points they can genuinely agree with.

Seems like changing from teaching sub to admin might require different skills.

You are going to work your way through this. Can you get one or two day admin subbing jobs for example? What did you do well? Then get one week appointments, then six months. Really there is no magic. Just doing it, and not blaming yourself for the bad runs.

Doesn't matter at all if you had poor classroom management if you're not applying to be a teacher: although managing some bosses might require similar mindsets lol. What skills did you use caring for your mum? Organisation, patience, that kind of thing? Is there a professional in your acquaintance who could vouch for you being well-organised and patient?

Oh, this as well. I literally tell my references what I need them to say. They know what the gig is, and they are totally okay being coached on what I need to come across.