Clemens:
Perhaps relevant for your initial problem: Can you charge the tablet form a power jack? If so you can try to use a combined notebook power supply with additional USB power out. E.g. http://www.conrad.biz/ce/de/product/515004/VOLTCRAFT-NPS-90-USB-Notebook-Netzteil-Laptop-Netzteil-BASIC-LINE-12V14V15V16V18V185V19V195V20V21V22V-/ So you can drive the tablet by power jack and the Arduino via USB - if 5 V/1 A via USB fits your need.
Sadly I can't! It only charges through the USB connector.
CrossRoads:
If you ran both thru diodes, the source with the higher voltage would reverse bias the lower voltage source's diode and keep that source turned off.
So if I understand this correctly - if I have a 7.4V battery and a 9V power adapter, it would use the 9V power supply by default? But what would happen if I used a combination of a voltage regulator (L7805) and a few diodes to bring the voltage of the power source down. Because I need 5V for the arduino, and I also need 4V for the tablet.