Me n mrs G have a bike each and looked into a carrier similar to that, in the end we opted not to bother and make do with either strapping the bikes to roof bars in a roof rack sytle. Or removing the front wheels, drop the seats and place both bikes in the boot/through space to the back seats, not an option for you I guess with the child seat in the back? Maybe put the child seat in the front?
No matter what you do it's going to be aggro. The rack in the link covers the number plate meaning a pull from the plod, the weight will mean the boot won't stay up and damage to the boot will inevitably result anyway.
The ones that carry the bikes clear of the number plate sit too high from memory, meaning opening the boot means possible collission with the rear window and aerial, more damage. I used roof bars purely because I already had them, and drove off to the woods with a mate similarly loaded only to watch him drive through a car park entrance in the new forest with a hight restriction and almost wipe the lot off the roof onto the floor.
If the bikes are outside the car they can be stolen more easily and mud falling on the roof will scratch the paint.
So in the end decided no matter what you do it's a pita, so why spend money on top of it all, so we stick two bikes in the boot....just. :-/