Most home health aides are considered employees of the person who hires them. If you hire your mother's aide yourself, then you're responsible for withholding and paying all the relevant employee taxes, including payroll taxes, Social Security taxes, and other mandated withholding in your state, such as unemployment insurance.
If you want to avoid all that red tape, the best way is to hire through a home care agency. The agency is the aide's employer, so it's responsible for following the proper tax rules.
Unfortunately, hiring an aide through an agency will generally cost quite a bit more than if you do the hiring yourself. When you use an agency, you're essentially paying a surcharge for the convenience of someone else doing the background check and filing the necessary paperwork on your behalf.
Because it's less costly, some people decide to hire the home health worker themselves but to pay the aide under the table, without filing any tax or Social Security forms. But they're taking their chances that they won't get caught by the Internal Revenue Service and have to pay penalties and fines.
If you do get caught, don't bother trying to argue that your mother's home health aide is really an independent contractor -- 99.9 percent of the time these workers meet the Internal Revenue Service's definition of employees, so this argument won't fly if you get audited.