You do not have to sync the iPhone apps. You can select the content that you want to sync to the iPad and to the iPhone. You do not have to sync your entire iTunes library to either device. I copied this from another discussion explaining how a user and his wife can share an iTunes library but still sync only the content that they want to sync to each device.
First turn off auto sync in iTunes. Launch iTunes on the Mac and go to iTunes>Preferences>Devices>Prevent iPods, iPhones and iPads from automatically syncing. Click OK and then quit iTunes.
Connect one of your devices to the Mac and launch iTunes.
Click on the device name on the left side under the devices heading.
Click on a tab in iTunes - Apps for instance.
Click on the Apps that you want to sync to that device.
Make sure that the Sync Apps heading is checked.
Follow the same procedure for all of the other tabs in iTunes ..... Music, Photos, Movies and so on.
After you have finished making all of your selections, click on Apply in the lower right corner of iTunes.
When you are done, eject the first device and do the same thing with the other device. iTunes will now remember the sync configuration on each device.
You can change that configuration any time that you like by following the steps outlined above.
If you want to continue to auto sync, turn it back on in the iTunes preferences as described above.
Something like this should work for you as well.
The new iPad, iOS 5.1, 64GB WiFi