Is your sister's hoarding causing the plumbing problem or making the damage worse? I'm imagining a situation where there is junk in the area where the leak is, which prevents them from cleaning it quickly and then the mold is much worse. That would probably be deemed something like "failure to mitigate" on your sister's/mom's part. It is the landlord's responsibility to fix the issues, but it is also the tenant's responsibility to take reasonable measures to prevent the problem from getting worse.
Although I can't imagine any landlord/property owner that would be ok just letting this go! Do you have documentation showing that they notified the landlord about the problem? The landlord might be trying to set up a situation where they can claim the security deposit or go after your mom and sister for the damage if they failed to notify. It would be really unusual for a landlord to risk their property that way though. Good luck!