You need to develop contacts and a good reputation (imo, a course won't do this for you, not for the kind of niche hours you're looking for)
Take a job, any job. Care work, seasonal work in a supermarket, kitchen porter in a restaurant, few hours in a coffee shop - whatever you can find locally. Then be flexible when they need someone to do extra hours (have a standby baby-sitter on call), or someone to do an admin job, or someone to step up into someone else's shoes when they're off sick for a couple of days. Show that you are reliable. Show what you can do.
Volunteer. If you've been a SAHP (with one household salary) for 10 years then surely you can continue on that basis for a while. Same as above - develop a good reputation, take on extra tasks, offer to do a couple of hours paid work if there is a crisis.
Make sure your dh/dp is on board with what you're doing and is 100% supportive. No point in you getting an afternoon/evening Sunday shift if he's not willing to look after your dc. And not as a one-off, to do that every week if needs be.
It you're good, and lucky, then after about a year you will have some recent experience to add to your cv, you'll have a couple of references, you might have learned some different skills. You might find the kind of 'gap' in the current job market where you could fit in. Importantly you will have people who know you.
tbh you are looking for the holy grail of jobs, and without recent experience, up-to-date references or flexibility, you are facing a really tough challenge.
Your youngest is about to get some care hours. Use the next 2 years (and yes, I think it might take you that long) to build your skills, your contacts, your network so that when youngest dc goes to school you are in a much better position to apply for (and get) the kind of role you are seeking now. You need to think and plan long term on this.
A couple of examples to show what you're up against:
My SIL had a high flying, high paid job - nannies, international travel etc. A sudden onset disability for one of her dc meant she could no longer work in the same role. It took her 10 months to find a job that she could do part-time and school hours.
dd's friend (who had professional accountancy qualifications and experience) had 2 dc very close in age and had been a SAHP. When dc2 was about 18 months she took a job in care support (minimum wage) - hours to suit when her dp was at home. This gave her a reference to move to a care/admin role in a charity. She took on a responsibility for 'centre management' on alternate Sundays - which mostly involved cleaning toilets and floors, but also included some significant admin and security responsibilities. Those roles enabled her to apply for a mainstream admin and facilities post. Then she took on some of the book-keeping work. Her dc are both now at school and she has an accounts role that works flexibly round school hours.