Christin,
As described you are not running a business out of your home, as such, you don't have a home-based business. Your father may...
You don't indicate what the situation is with your father's house. But, in essence, anything which you want to claim as an expense is income to him. You would have to set him up in business as a landlord from whom you are renting space for your business. He (maybe you are the one doing the paperwork) might claim that he is renting 1200 square feet to you, or 4 rooms to you, etc., and offset a percentage of his utilities and other expenses - related to things that you actually use, as an expense against the rent that you pay him. This would be handled on a Schedule E filed with his taxes.
An interesting twist here is: if you and your father are very close and sharing resources, a number of things can be done to minimize tax liability. If you are in a higher tax bracket, you could pay more rent for the space, effectively transferring the income to him. If he is in a higher tax bracket, you'd want to balance everything and make your rent equal to the expenses that he can claim against it.
Essentially for the IRS, this would be a reasonability issue. If you have 6 daycare customers providing and income of $50/day/child for a gross income in the range of $75K and claim $5K/month or $60K/year as rental expense, they are not going to believe it. If the claimed expense is more in sync with local rental rates, it'll fly.
But, to reiterate, whatever you claim as an expense is income to your father's rental business.
If, when you look at the numbers or for other reasons it doesn't make sense for you to do this, just ignore "facility cost" and pay your income tax based on what you took in and paid out to others.
Caveat: Please don't take this as legal advise, but, if it helps you get very rich it's okay for you to share a little of it with me.