I just did all of that...
You can use any battery charger you want, but be sure to wire the charger on a separate circuit off of your main distribution box otherwise your inverter will end up powering your charger.
Then you'll need some type of multiple source relay transfer switch. The IOTA-30R should be plenty for your needs: http://www.iotaengineering.com/pplib/30rman.pdf
If your Univolt also acted as your circuit protection, you should also install a fuse block to protect your 12V
devices. The Blue Seas 5025 would satisfy the requirements:
ST* Blade Fuse Block With Cover - 6 Circuit with Negative Bus - PN 5025 - Blue Sea Systems
The fun part will be fishing the wires where you need them...