Yes. Get a portable--mono--radio. Feed something mono into the program line. Does your audio sound weak? You have the phase flipped on one feed.
Another clue is available on your stereo generator/audio processor if you have metering of the L-R signal. With a mono feed, you should be able to "null out" the L-R signal by adjusting the input level of one channel. If you can't do this,(on some multi-band processors it is difficult to get an exact null) but more importantly, the meter shows considerable audio level, you have a phase shift.
To get rid of it you simply switch polarity on one input. But since you are hearing this only when you switch studios, you need to check each studio to see if the outputs are wired correctly.
Most folks use single pair shielded audio cable, red and black wires, by convention, the black wire goes to the (-) output, the (+) has the red. If someone was careless about wiring the console outputs, it is easy to flip one pair and create your phase shift. Some folks like to use 4 wire cable with two individually shielded pairs, black and red; white and green. This is where your phase shift can come in--installer "A" uses white/green for left, with the white connected to the (+) output; installer "B" uses the red/black for left, then connects the green wire to the right (+) (which also switches channels!).
Doesn't matter which is "correct," but it is important that whatever wiring scheme is used that it be consistent.
My bet is you will find the flipped wire in your studio switch.