No doctor
Her mother ^bought herself 80 grand's worth of living space which she has parked for free on OP's property. She has benefitted from garden space, use of OP's* kitchen (and probably the house space if she is turning up the heating when everyone else is out), free "taxi service" for shopping and appointments, low "rent" and utilities bills etc and company when she fancies it, privacy when she doesn't.
In return for this she has continually left the kitchen in a mess, doesn't do any garden maintenance but enjoys use of the space, complied about OP's parenting style, only reluctantly help OP" out with the children - her OWN grandchildren in emergencies, come and gone in OP's* home as she pleases and repeatedly held the threat of taking 'her| money back whenever there has been a dispute.
She sounds a cow. Get her out OP - this will cause trouble between you and your DH, and you and your DCs, (I can practically promise this will happen - my parents were in a similar situation when I was young, and my Evil Grandmother operated a "divide and conquer" policy, playing one off against another) and as others have warned, will get worse instead of better as she gets older and less able.
Get her out now, while you still have your mental health!
If the money is legally yours, then let her whistle for what is "owed" - why should you have to move house and uproot your children if you are happy where you are, when she is the one causing problems?
If you are legally (not ethically) obliged to pay her something, then get a loan, increase your mortgage, sell your soul to Lucifer - but get out of this situation asap.
She is in a very powerful position, but only because you are allowing it. You hold the cards in this situation, but she isn't letting you see that. She's bluffing.
Honestly OP - even if she seems to agree to pay more/ keep her nose out of your business/ clean up after herself/etc - I would do something now because otherwise you WILL end up as her carer, she will become nastier and nastier (people always become more themselves as they age, when social niceties matter less to them) and you and your family will have dreadful lives.