Hazarding a guess, you may have to remove the laptop from the company domain and use a Workgroup instead to be able to connect to a home network. Right click "My Computer", select Properties and then the Computer Name tab. Is there an option to change the Domain to a Workgroup? (I don't have XP Pro installed to be able to check.) The Workgroup name has to be the same as that on the desktop PC.
I wouldn't be too concerned about mapping network drives, initially you want "each" PC to see an icon for "both" PCs in My Network Places.