Sharon,
In my personal opinion.
First thing first, resolve Ice-maker issue by removing the water line from the back of the freeze and offer her one-time $20-50 off for inconvenient (usually you don’t want to give incentive, else they will complain more often). Also ask her that you are concern about her health/safety and therefore you must inspect the Ice-maker ASAP before mold start to progress.
Once this issue is resolved. Check your local law about pets and vaccination (call your county to find out). Consult an attorney to see if you can kick her out ASAP. I think it might be worth having an attorney draft the letter with their address and send it to her.
Another option is to offer her one month free rent if she moves out by X date. I have done this once where I am glad it’s over.
Next time – have $50 per month incentive for no service call. Also like what Jake said include 30 or 60 days’ termination clause (check your local laws).
Good luck!