If the database on the old and new computers have the same names then when you restore on the new computer it should ask whether you want to overwrite or create a new database.
Either way, you are likely to want to add the hands from the second computer into your main database anyway, I expect.
What I would suggest is to copy the hand history files from your second computer to the first, and import them to your database there (using Get Hands From Disk), so that when you backup/restore your database they would be included on both computers.
This will put the database in both in the same state, and then if you sync them after that they should stay the same.
The hand histories should be in the "Processed" folder, which you can access via File > Open User Data Folder in the PT4 menu.