Review your rental contract, consult your local tenant's union, consult the housing board. Ask the latter two if they can connect you with any legal resources, and see if you can find a human-readable version of your local housing ordinances. It's very likely
- she can't take it out of your security deposit unless you're moving out; a deposit is not a savings account she can pull from, it's a way for the leech to make themselves whole at the end of a contract
- you're not responsible for the damage or the repairs thereof unless you broke something to make it happen or your rental contract specifically states that you are; if the contract does say you are, then she shouldn't be contacting anyone to fix it, anyway, since you would be the party responsible for fixing it (and can therefore find the cheapest contractor in the area to fix it)
- she may be doing something illegal in all this, which might be in your favor
- if she does insist the sink be replaced, she's the only one paying unless you sign something saying otherwise
Landlords are also not supposed to be just "dropping by", so check the notice period in your rental contract to see if she's in violation.
Do not perform any DIY, or you will become liable. Do not spend any money or sign anything related to this matter without legal representation. Do not volunteer your resources in any way or admit fault. Do not let your landlord enter the premises without notice, and definitely do not let them poke around the place without notice. Cross-check everything in your rental contract with the tenant rights protected by your local housing ordinances, since leeches love to write an illegal contract.