Powering Arduino and sabertooth from 2 separate batteries (12V and 7.2V) ?

Hello guys! I’m a new Arduino user and looking on a good way to power my new robot.

I have:

Arduino Uno USB board
Sabertooth 2x5 motor controller
2x 12V motor (2A max)
LCD shield (4x20 from DFRrobot)
PS2 Wireless Controller
Some sensors…
2 Batteries, both NiMH (7.2V and 12V)

And here is what I intend to do. Is there anything bad in this setup? I’m not sure the 5V/100ma from the sabertooth is enough to power arduino with LCD,so I use a separate battery. This will also isolate both power supplies. And the 7.2V battery should not make the regulator overheat I hope.
If any advice/tip can be given, I will gladly take them If it seems good, I’ll try it as as soon as possible! Thank you!

If any advice/tip can be given, I will gladly take them

Connect all the grounds.