HOW DO I ADD MY IPHONE TO A NEW/SECOND COMPUTER SO FOR ITUNES?

If you haven't synced you phone with iTunes before the first thing iTunes will do is delete all iTunes media (apps, music, podcasts, etc.) from the phone, then replace it with the media in the iTunes library you are syncing with. Establishing syncing for the first time without losing your data has to be done carefully. This guide will give you the process for doing so: https://discussions.apple.com/docs/DOC-3141. There is a related guide here as well: https://discussions.apple.com/docs/DOC-3991. However, as covered in these guides, only music purchased from iTunes can be transferred from your phone to your iTunes library. Transferring music from other sources from your phone requires 3rd party software such as Touch Copy.

Other options:

If all your music is purchased from iTunes, it can be download directly to your phone for free without syncing (see http://support.apple.com/kb/HT2519). Another option to get your music without syncing is to subscribe to iTunes Match (seehttp://www.apple.com/itunes/itunes-match/). This will scan your iTunes library, match songs already in the iTunes store and upload any songs in your library not in the iTunes store, then make your entire music library (up to 25,000 songs) available to download from iCloud directly to your phone. (With iOS 6 due out next week on the 19th, iTunes Match songs can also be streamed to your phone without downloading and taking up space on your phone.)

You could also clone the current library from your parent's computer onto your laptop. This would still be recognized as the "home" library for the device. You could then remove any media you don't want to make way for more...

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