I think one of the problems you will encounter is consistency. You might have 5-10 parents that want to use it 1 day and you would have to staff accordingly for that day, then another day where no one will use it. How would you plan for that? You said you plan to use college students to fill the gaps, but you would have to check your states laws if that is even allowed. Some states require all daycare providers to have some sort of licensing.
I would recommend starting with in-home services at first and see how it goes. You can confine the dog to an area where there will not be any contact with the kids.
If you are set on buying this duplex building and doing something kid-related with the other side, maybe open a drop in playgroup. Something for rainy days, homeschoolers, SAHPs, Nannies, etc. You can have a coffee station, snacks, story time, craft time, and sell punch cards for visits. Change out the toys and stations, etc. Provide a changing area, comfortable seating for nursing moms, etc. You wouldn't have to worry about state ratios because the parents would supervise their own kids, then you could hire a college student to lead various group activities, or act as a mother's helper.
ETA Option: You can also talk to the other facility on the other side of town about opening another location on your side. Think of a franchise model. They have already done the leg work and know the ins and out, plus pricing. Figure out how to use their knowledge and expertise instead of trying to recreate the wheel.