The parking isn't actually free in my experience. You can get a lower hotel rate without the parking. When you ask for the rate with parking the price goes up, often comparable to booking the hotel separately and paying separately at airport park n fly spots. But the convenience is worth something.

I suggest you ask your hotel this question. However my recommendation is to find out which hotels are listed on Park sleep fly. Then just call that hotel directly and book through them. My experience is that the same hotels will offer you free parking for up to 2 weeks if you stay there at least one night. Generally, the cost ends up being just the same and you don't have to hassle around with Park sleep fly