I am sorry for what you are going through.
Make sure you keep all whatsapp messages.
Suing will cost you even more time and lawyer's fee and giving statements, you really don't want that especially if you are cariing for your mother. Your lawyer's fees will be more than $12K
You can get part time professional help at some agencies like bamboo nursing (I have used them before). You can hire the health workers which are reasonable hourly rates or quality health care assistants.
After reading what you wrote, I would ask for a refund and not trust anything that this agency sends you.
First, find temporary care for your mother so that she is taken care of.
Then,
Make sure you write an official letter to them detailing all of their refusals and post it to them registered mail so that they have to sign for it. Then they cannot turn round and say you never asked them for a refund within 5 days. You have to be reasonable. After you send the letter (make sure you have a copy), and go visit them on a sunday with a copy and ask for your money back.
Visit them on a sunday (their busiest day for making money) and ask for your money back. Make sure you send copy of letter to immigration department regarding this along with the employment contract department and write that on the c.c. It might well be that the helper you signed has now been assigned to someone else.
If I were you, I would also visit immigration department about your application. You might find out that it was never even submitted !
It will take several months to find a helper so you still need to find temporary care first.
PM me and I can recommend a good agency. He's a one man band agency but he's good at paperwork and always keeps me informed.