If you hire your parent to be the caregiver of your child, you are correct that you do not have to issue a W-2. The parent will file a tax return and will write in the amount of their income on line 1b. They will not build up any credits in the social security/medicare system. If they file a joint return with their spouse, they won't owe income tax if their income is less than the standard deduction, including the adjustment for over 65. See here.
https://www.forbes.com/advisor/taxes/standard-deduction/
Because there is no paper trail (no W-2), and because it is very easy to claim fake income to get insurance credits, EIC, or other benefits, I believe this is an area of higher than normal scrutiny for the IRS. (For example, it is a known scam for incarcerated persons to file false returns claiming income with no W-2 or 1099 for purposes of qualifying for false benefits.) You will want to make sure your mother is paid using checks, or some kind of electronic draft that leaves a clear trail that can be shown to an auditor as proof she worked for you and was paid for that work.
If you hire your father as an independent contractor for your small business, you will need to issue a 1099-NEC if the amount is more than $600. You can deduct the payments as a business expense. Your father will have to file a tax return that includes a schedule C for self-employment. He can deduct ordinary and necessary business expenses, if he has any. He will pay 15% self-employment tax on the net profit from the business even if his total income is lower than the standard deduction for income taxes. He will get credit in the social security system for the work. This income would also qualify your father to contribute to an IRA.
I think the short answer is that paying your father results in less tax for you because it is a deductible business expense, but more tax for your parents because of the 15% self-employment tax.
I don't deal with ACA insurance and the affordability credits, so I can't tell you if that amount of wages will enable a credit sufficient for your purposes.
I am slightly concerned that you are setting the wages based on the need to acquire insurance, rather than the value of the work performed. In case of audit, you may want to retain proof that the monies were actually paid, that work was performed, and that the compensation was reasonable for the level of services performed.
