If you want to keep one at ther house why not just buy it online and ship it to them? It would be one less thing to carry on the plane. I'm pretty sure you won't be able to use the base on the plane because the seatbelt would interfere with the car seat clicking into it.
Most infant carriers are easy to install baseless so you might not even need a second base.
Yes, that was the plan if we decided to get a second one. We wanted to make sure shelling out the extra $70 made sense.
I didn't know you could install car seats into cars without the base. We'll plan on doing that unless we find we can't do so with the Britax B Safe.