1) Get docks for home and work, so it's just one step to connect peripherals. It's actually a lot more convenient than having separate machines for work and home.
2) Find out if you can use a virtual desktop setup, where everything is running on your work machine, but you can use RDP to control it. A competent IT dept should be able to set that up in a way that's not less secure.
3) If you're in the US, your company can't force you to carry a heavy laptop if you have any issues with strength or mobility. If you want to exploit this, you can ask your doctor for a note saying that you shouldn't carry a laptop to/from work. This is actually probably true for the many people who have issues with back pain.