If she moves and we want to rent the home out, can we (parents) treat the home as a rental property even though we don't have ownership?
No. You can't rent out that which *you* do not own. It would be like you trying to rent out a room in *my* house. Not gonna fly.
The home would be in her name and we'd be non-occupant cosigners on the loan.
I guess everyone has their reasons - but I can't figure it out. If you are buying the home with your money and putting your daughter's name on the deed, then it's a gift to your daughter. You'd need to file IRS Form 709 - Gift Tax Return since there's no doubt the gift is worth more than $15K.
Just purchase the house and keep everything in your (the parent's) name. Later down the road of time if you want, you can sell it or gift it to your daughter. But understand that once the transaction is closed, you can't make any changes to the property ownership without the permission of the mortgage lender.
