Hmmm, well if I understand your question then, Yes, you can connect to as many domains as you wish with a PC, laptop or whatever.
You will have to setup your laptop to log into a domain first. Then, after rebooting, just log into whatever domain you are currently at.
Now, you have to setup that computer and your user account on both domain controllers...both at home and at work.
If you don't already have a PC at home setup as a domain controller then you have to assign a PC for this task.
Or you can just log into the domain at work when you are at work and when you are not at work log onto your local machine name as the domain name.