Can/Could a Split Brain computer be built?

So, here's my dilemma. 90-99% of the time I'm sitting at one desk doing my work, but the other 1-10% of the time I need to travel -- visiting family/friends, working on site with clients, taking my kid on a vacation, conferences, etc.

If I can't take my work with me, I can't travel as much, so given that I like mobility, so far I have only been able to figure out how to make work work with a laptop (Dell Precision mobile workstations).

However, 90% of the time my laptop is docked and functioning as an overly expensive under powered desktop. The other 10% of the time it is really heavy but quite powerful laptop.

What I'd really like is a "split brain" computer. A decent but not necessarily workstation powered laptop that docks into a powerful desktop and when it is docked swaps state and control to the desktop motherboard/CPU/etc. There would have to be redundant motherboards/CPUs and likely GPUs and ram. Ideally the setup would efficiently use all resources available when both brains are together, but even if the full mobile brain has to go dark when docked that would be fine.

The closest I've ever seen to something like this is a guy who has a virtualmachine that he keeps synced between home, mobile, and work by putting the machine image on dropbox.

Does such a thing exist? Could such a thing reasonably be built?

Thanks.