How to Combine iTunes accounts
Ideally you create an additional user account for yourself on the family Mac. Of course this will lead to having two copies of specific tracks and apps on the disk but overall it's much easier to handle than trying to combine two accounts (or handle two Apple IDs/ITS accounts from within one iTunes configuration).

For additional information concerning the migration see


iTunes: How to move your music to a new computer
How can I switch the computer I sync my iPhone with and keep my apps?