I don't think it works that way unless you are a car dealer- when you get the title signed into your name, you will need to re-title it and pay the sales tax unless you have a dealer number. If you are getting a loan w/ a lienholder, that's more paperwork.
A few other thoughts- put this on craigslist for a higher price for one week and see what happens (yes, I've had toddler twins, do it anyway). Why give that money to a car dealership? If you don't want a great deal, pass it on!
Are you sure you don't need or want to upgrade your own vehicle? I have no idea what you drive, but be sure you don't want to sell your other vehicles and upgrade before you just sell it off. A 2014 would have many years of good driving in it if you will be needing to get a newer vehicle as your kids grow.
I find it really tacky to say you will buy it w/ the intention of selling it the same day- they are doing you a favor by selling it cheaper. I would just say no if I wasn't interested in using the vehicle. You will need to mess w/ the loan/lienholder thing, registering vehicle, paying sales tax. I don't know, but it just feels wrong to me.