And right here is the problem...
"do you want erase all music ... On this iPad"
SYNCING your iPad is different than BACKING UP your iPad.
You can only SYNC your iPad to a single device. You pick your desktop / laptop you plan to sync with, and you stick with it. Your music collection is tied to that device.
You can BACKUP to any device you wish.
If you are getting the above message while you think you are backing it up, you're doing it wrong. You're syncing the device, which is not what you want.
If you are losing your music collection when you "backup", it's because you are SYNCING the device, and not syncing it to the same machine with which you originally paired it with.
I have two iPads in the house, 4 iPhones, and 3 MacBooks. NEVER have I experienced the nonsense you're talking about... you really should take the time to learn to use the thing correctly before crying "it's broken and I hate Apple" on the web.. haha.