Living hell
What about going up to her and ask her for the money whenever you have to buy her things? If she doesn't pay, don't buy. Or pass her the receipt after the purchase and let her know that while she has the original receipt, you are keeping record of it too. Do all that with a smile, never raise your voice (or others will fault you for that).
Next time she complains about your cooking, tell her to take over since she's an expert. If she complains that she doesn't have the time because of her coming exams, tell her sweetly, with a huge,
understanding smile that that's too bad because that means she has to bear with your cooking.
And if she ever badmouths you in your presence or behind your back, just smiles and listens and says in your sweetest voice that despite all your faults and shortcomings, you don't badmouth untruths about people and your heart isn't black. You can even go up to her and...no, I shouldn't be teaching you that, it's spiteful.
Never throw your temper, don't get angry (I know it's tough) or you will be perceived as an ungracious host/unreasonable sister-in-law who makes her life difficult while she's trying so hard to pass that
obviously difficult exam.
Who knows, if you keep smiling whenever she's being difficult, she may even start thinking you're truly crazy and leave you alone
Your mother may get you to give in because you're her daughter, not her. Don't know, just a thought.
I thank my lucky stars I get along reasonably well with my sister-in-law.