You are going to run into trouble if you need three car seats. I doubt they will fit in a standard towncar. You may have to go with a van or a true limo. There is room for four usually....without any car seat. Three in back, one up front with the driver. But, as I said, you could book a van through one of the car services.
If you use the DME (Mears run), there is no need for car seats. Actually, you can't use them as there is nothing to attach them to on the bus. If it were me, I would just use DME. But, I'm usually happy with the service I get from DME.