Thank you for being a caregiver to your mother. Care giving is a huge responsibility that requires significant mental, emotional and physical effort.
From the tone of your question, it appears that the money in the joint accounts is your mother's money.
Hire an Elder Law lawyer in Gloucester City to help you. In order to receive money that is not considered by Medicaid as a "gift" it will be to your advantage to have a Caregiver Contract that complies with NJ Medicaid provisions, so that your are compensated for your being your mother's caregiver.
I assume that your mother has been paying the nursing home charges with her own money. Nursing homes like private pay patients because your mother is paying the full price and not the network negotiated price Medicaid will pay. It sounds like the nursing home is encouraging your mother to "spend down" (a Medicaid term) her cash resources in order to qualify for Medicaid. It is a little late to be making Medicaid planning decisions. Nevertheless, I recommend that you contact a qualified Elder Lawyer in your area.
Please remember that this is a general response to a general question and that you have simply made an inquiry. This attorney answer to your question is for general purposes only and does not establish an Attorney-Client Relationship. This attorney response does not obligate the attorney to provide you with legal representation. Submitting this inquiry and receiving an attorney response does not create an Attorney-Client Relationship.
I would suggest you go immediately to an elder law attorney the specializes in Medicaid planning. They are best suited to answer your questions and will lead you down the right path. There can be planning that can be done to preserve some of her assets, but you want to do that as soon as possible to not miss out on any possible opportunities.
I am an elder law attorney who handles Medicaid applications in New Jersey. You need an attorney to go over these issues in detail with you, and analyze the bank accounts to see if any of the funds expended from the account can be traced. There is a presumption that any assets you spent will go toward a penalty period where your mom won't be eligible for Medicaid.
It is very important that you talk to an attorney (if not me, someone else) to preserve your rights.
This answer does not create an attorney-client relationship. In order for you to establish such a relationship, you will need to pay an attorney who is licensed in the state you're currently living in. Feel free to give one a call and ask them, in order to get a more detailed answer.