Finding the voltage across nodes A and B
Your simplified schematic is incorrect. You can't ignore the 6-ohm resistor.

The key point to realize is that there can be no current through the 5-V source and 10 ohm resistor, because there is no return path for that current. That lets you calculate the potential difference between X and Y very easily.

Potential differences A-X and Y-B can be found by applying KVL on the two loops in the circuit.