Is my Mom entitled to around the clock aide?

When the care level becomes 24/7, it is cheaper for Medicaid to pay for a nursing home. Have a long talk with her doctor, because he is the one who orders in home car. Discuss the options for her. Please accept the reality that limited mobility and limited brain function is not "fine" but requires an intervention.

She can hardly walk and functions fine? Dementia becomes worse with time, and it will. Are you her POA? Your job is to provide her funds for her needs and wants if she cannot do for yourself. If she does not have the funds then Medicaid is necessary and you job to get that application done.

Entitled? Yes if that is what she wants!

If she wants one and has the ability to pay for it.