I own a property in Los Angeles which has had plumbing issue with water flowing back from the toilets and this issue has been going on occasionally since last year. I spent 7000$ initially to change the plumbing line ...

For a less seasoned investor, this can definitely be a threat.

If you have that done then the rest is, as others have said, idle threats.

Hope this month turns out similar to last month for most where the threat of no rent is more bark than bite.

I think one of the biggest problems I saw in folks' complaints, while working for an AMC, was undue influence via threats of complaints to the Appraisal board for no good reason or jamming objectively bad comparables down their throats and demanding they are used.

One of the property managers who shares information on some of these threads posted audio of a death threat they received by voicemail.

Assume they have weapons.The greatest threat of weapons in a home is to the gun owner and their family not the landlord.

Even the threat of going to their insurance may be effective in getting the repairs. 

Ignore her childish insults and threats.

This may be only a threat to try to push your hand.