If I enroll my mother in Long-term Care Medicaid insurance to pay for adult day care, in-home care visits etc, will my mother lose her social security check?

The problem is this:
Medicare only pays for SKILLED nursing services in the home or any other venue for that matter. SKILLED care is care ordered by a physician and rendered by skilled professional such as a Physical Therapist, Occupational Therapist, LPN, RN, etc. At home, these services are intermittent in that the provider will come to the home, provide the service and then leave.
Whilst receiving skilled care the patient may also receive intermittent the personal care services of a home health aide once or twice a week. These personal care services end when skilled services end which occurs once the patient has stabilized or no longer progresses with in home therapy.
Under no circumstances does MEDICARE pay for custodial care.
If long-term custodial care is required, MEDICAID or private pay are typically the only options.
Some states due have Home and Community Based Services (HCBS) under their Medicaid programs. How her income will need to be handled will depend on the state in which you live and the program she enters.
In my state, Florida, most receive HCBS under what is known as "Diversion". In this program the beneficiary keeps her/his income.
Hope this helps...God bless and good luck.

This is an Elder Attorney question. Get a referral from her CPA or her insurance agent.