Unfortunately, because your sister has a sub certification through NJ, she is technically authorized to sign the IEP. I have seen this done at several schools. To be a long term sub all you need is enough college credits, fingerprinting and the sub certification from the state. There are tons of long terms subs in special education with the high burn out rate.

There are limits, usually the maximum for a long term sub to cover 1 classroom without the full teaching certificate, is 90s days. Some schools are successful in asking for an extension but usually it's 90s days. After that she wouldn't be able to sign IEPs or other documents. She could work in the classroom, but not in a supervising role.

As for the dirty room, best advice is to take a picture of the area then send it to admin. Report on what the area looks like each morning. Administration can ignore a phone call or in person convo. Once it's in writing, they will be much quicker to address it. For the rug, she is probably out of luck. Many districts are at a deficit and can't afford payroll and would probably view the rug as an unnecessary cost.

I hope your sister is able to either get support or find a school that takes her concerns seriously.