If you pay someone who works in your home a wage for services performed, they are a household employee. This includes a maid, nanny, etc. If they work in your home according to your schedule, they are your employee, regardless of your relationship or where they live. Here is the tax guide for household employees.
https://www.irs.gov/publications/p926#en_US_2023_publink100086740
Generally, you are required to issue your household employees a W-2 if you pay more than $2,200. You are also required to pay household employee's tax on your tax return -- this covers social security tax, medicare tax, and unemployment tax for the employee. You are not required to pay household employees tax if the employee is your parent, unless the parent is providing child care services for a child under age 18 or a disabled older child. If your second child is old enough that they do not require child care services, then you can pay your mother any wage you like for household services and you do not have to pay household employee's tax. However, you must still issue a W-2.
In general, a single adult can earn up to the standard deduction and not pay federal income tax. The standard deduction for 2023 is $13,850 plus $1850 if over age 65. However, if your mother has other income, this may affect the calculation.
Because she is not subject to household employee's tax, she will not build credits in the social security system for disability or retirement. That may or may not be important, depending on her age and expectations of future work.
There is no reason you need to do this. As pointed out, this can just be family living together helping out with expenses. You get no benefit from paying a salary, and your mother doesn't really get any benefit from receiving a salary, unless she needs it to show eligibility for something legal (a loan, citizenship, insurance subsidies, etc.). Under some circumstances, creating a paid position for your mother who helps around the house just to have a W-2 could even be considered improper.
If you didn't pay your mother a salary, you might be able to consider her your dependent. That would result in a $500 tax credit for "other dependent" on your tax return. I can't tell you how it would affect her ability to obtain medical insurance, that's complicated and I haven't studied the issue. Your employer may allow you to add adult dependents such as a parent to your employer-sponsored health insurance, it would be worth asking.
Lastly, this does not consider state law. If your mother is your household employee, you might have requirements under state law to pay taxes, issue check stubs, or pay minimum wage. You would have to check with the laws of your particular state. And, the taxable income threshold might be different (higher or lower) in your state than for federal taxes.
