Sorry if this is a bit disjointed - hopefully something will be helpful! I've tried to limit it to stuff that'll give you a reliable income, rather than Avon and Ann Summers 
Long term though, I'd seriously think about retraining OP
though I know with two wee ones it's not easy. In the mean time;
You could look into becoming an appropriate adult sitting in on police interviews, I'm not sure if this is still paid, I think of varies between counties. I'd imagine it'd be really rewarding and interesting if you want to help people.
Mencap post some really good home based roles on occasion, often for advocates (which I'd imagine would involve lots of letter writing!)
Again, not sure if it's always paid, but you sound like you'd make a fabulous union rep! Again, lots of letter writing.
Do you think you have enough admin experience to look into being an NVQ assessor?
With your letter writing, you could maybe look into running online courses on how to write and get results? I've seen a few sites where you can do this. Super easy to promote via groupon and Facebook. There was a really good webinar on this, I'll try to track it down.
GiffGaff often advertise for at home e-chat customer service people, which is perfect with little ones as you're pretty much silent when they're in bed with no noisy phone calls.
There are loads of remote based roles out there, and a lot of them are posted by charities. A few may be open to part time, so it's worth asking the recruiter (apologies if I'm not supposed to post links)
https://www.indeed.co.uk/m/viewjob?jk=54b485b79bc65ee0&from=serp
https://www.indeed.co.uk/m/viewjob?jk=25ef8fddda0480c6&from=serp