Being made redundant during Covid isn't unusual. That employer should still be prepared to give you a reference and that should count as your reference from your most recent employer.
A career break to care for a relative is also not unusual, even if you didn't provide intimate or health care you still did a wonderful and difficult thing motivated by love. If you describe that as a career break during which you had caring responsibilities, many employers now consider 'returning carers' as a demographic that is underrepresented in the workforce and will be considered favourably. Could your GP or your grandma's GP/hospital consultant/social worker/bank manager/vicar write a reference - factually if necessary - to say that you were her carer?
If you could take on some volunteer opportunity even one day a week, that would provide you with an up to date reference quite quickly. I wonder if there is any scope for volunteering at the school your kids recently left? Or at a hobby or after school club they attended? They will know you a little through your kids and that might help you get stuck in?
Or maybe you have actually done things like helping with fundraising through the PTA or giving lifts to help with school trips or sports matches, or decorating the hall ready for the leavers' prom - that the school would consider volunteering and be willing to write a factual reference saying you helped out?
Do your kids have close friends you've interacted with during their years at school whose parents might be willing to write a character reference for you?
Did the place that supports adults with learning disabilities say what kind of reference they would accept? They might be able to give you guidance if this is an area you'd like to work in.
Could you do some self-employed work related somehow to your old industry? Tutoring, proofreading, drafting documents, advising in some way. Even if you just did a few hours a week someone you helped would likely be willing to give a reference.
Or could you enrol for an evening class or similar as pp suggested and have the tutor write you a reference?
I don't think your case is hopeless. I hope some of this is useful and you find something you'd like to do, that works for you, soon.