Master bedroom switch must be on in order for spare bedroom lights to turn on
I fully agree that you need an electrician, but I wanted to place a guess on what may have happened, just for fun.

The problem was most likely made in the ceiling box in the MB. Someone obviously tied the switch in the MB to the switch in the spare room; so when you flip both switches on, the current is travelling through two switches then up to the spare room light. 

I'm guessing that the culprit is the black wire- it is travelling from the switch in the MB, to the light in the MB, and to the switch in the spare room. And (another guess) there is probably a cable connected to both ceiling boxes... the travelling black goes through the ceiling box in the MB to the ceiling box in the spare room and then down to the spare room switch. Then the white wire from the spare room switch will carry the power up to the light and I'd bet the end of it is wrapped with black electrical tape.

In the ceiling box of the spare room there are (guessing) two white wires connected to the fixture (one is probably wrapped with black electrical tape) and two black wires tied together (separate).

Now back in the MB, the power (the true hot) is connected to the red wire in the ceiling which goes down to the switch. When the MB switch is on, power flows through the switch, up the black wire to the ceiling box where the black wire is tied to both the light fixture and to the switch in the spare room.

And I'm guessing that the solution (in the ceiling box of the MB) is to connect the red wire to the light in the MB; and connect the black wire to the true hot, so that both switches have a hot wire.