I don't about her work notebook and the domain issue, that is something she/you need to take up with her IT people.
But for your home network, there's nothing nicer than having the printer networked. The printer does not have to be tethered to any computer. No computer has to be up and running for the other computers to print to it. No computer has to be set to share anything. The printer can be centrally located, off of someone's desk. And everyone can print to it at the same time and the print server will sort the jobs out.
Of course, you must have a network first, and for that, you typically need a router. Then you need a network ready printer. It will connect to your network, just like your computers do. If your printer is not already network ready, you will need a separate print server that connects to the router, then the printer(s) connects to the server. Some printers have them built in, some routers have them built in. If no print server, you can buy stand-alone print servers, such as one of these
Then on each computer, you will add a new printer, following the prompts to add a networked printer.