Not sure exactly what to put here.
My green card in law lives with us. I don’t give her any money directly but she doesn’t pay rent nor for food. ( She takes care of our kid ).
Is that considered Financial support and i have to answer yes?
You’re going to have to list this relative as living with you in section 18 of the sf-86. You might as well just answer yes to providing support as well. As long as this person isn’t a terrorist you’ll be fine. 
The answer is that, yes, you are providing financial support. The good news is that your explanation should completely mitigate the issue. You’re not sending money overseas and your not even providing spending money. The person lives in your home, provides a service in exchange for their room and board and you’re not sending money to someone in Yemen where you can’t actually see what the money is being used for.