The reality is that your family member is living with you and will help care for your children. This is something families have been doing since we lived in caves, and there's no reason to make a fuss over it.
Doing something on paper that is different than reality just to get a tax or other financial benefit, is usually a bad idea and can sometimes even be fraud. Do you really need the food stamps? If she has to claim rent to qualify, you may be committing welfare fraud. You may want to have someone review with you the laws of your state.
For federal income tax purposes, if you report that she pays rent, you will need to file a schedule E. You can deduct part of your utilities and other household expenses up to the amount of your rent, but you won't be allowed to show a tax loss since this is a relative and probably below fair market rent. Doing this will make some of the proceeds of selling your home taxable down the road, even if you normally qualify for the capital gains exclusion. Keep all your rental paperwork for at least as long as you own the home plus 6 years after you sell.
If you pay her $400 per month to watch your children, she is your household employee. You will need to give her a W-2 at the end of the year, and pay household employee's tax on your tax return which will amount to an additional 15.3% of her wages. She may or may not be required to file a tax return depending on her other income.
This is what you have to do to make it look on paper that you hired your mother who is also paying you rent. I wouldn't do it that way, I would just let her live with you and watch your kids. If audited, I would be afraid that it looks like a sham. You may wish to have the situation reviewed by a tax and law expert.
