"What does it mean that only backs up in bath 2 when tub in bath 1 is drained?"

If I understand you correctly, if this has always occurred since living there it may be that there's a vertical drain pipe connecting both drains and when draining a tub on one side the water takes the path of least resistance and will bleed over to the other drain, perhaps even with no clog.
Either that or the clog is on a lower level.

I'd run a snake down the vent pipe from the roof, and make sure it's long enough to reach to the lowest level. I prefer to use powered snakes as they do a better job of snaring the hair clump that may be causing the problem.
JMHO

You can not snake a tub fixture arm through the tub drain. When you insert a snake in the tub drain it will only go to the Tee of the Waste & Overflow. The correct way is to remove the overflow cover and if you have a lever lift drain stopper you will find a wire connecting linkage attached to the lever on the back of the overflow cover. Pull that linkage up until you can pull the stopper out.

Snake the drain through the overflow and it will go straight down through the tee to the trap and through the trap into the fixture arm.

Here is a easy 5 step approach for dealing with clogged drains.

1.Remove the strainer from the drain. You should be able to remove the screws holding the strainer in place and pry it off easily.
2.Remove any hair or other materials from the strainer. Also, thoroughly clean off the top part of the open drain.
3.Place the plunger over the drain if it is still clogged. Push down on the plunger and allow it to come back up. Do this for one to two minutes. Run water over the drain to see if the clog has broken up.
4. Pour a chemical cleaner down the drain. This can also help break up any clogs. You can use a brand such as Drano, or your own solution of one cup of vinegar mixed with one cup of baking soda.
5. Replace the strainer once the water is running through the drain with no problem.0

If you are in the Los Angeles area try a plumber in Tarzana.

Tarzana Plumbing

Here is a link that might be useful: Tarzana Plumbing

According to my experience there are mainly 5 reasons for clogged drain. The first id grease now most of you will think what damage can grease cause, isn't it supposed to be a lubricant. I had asked the same questions, but then the plumbing guy from Hy-Pro Plumbing and Drain Cleaning, Ontario expalined that if grease cools it can solidify and create blockade. Next is paper, it can be any paper product, such as paper towels, cigarettes, and feminine products. They do not breakdown and cause block in the drain.
It is especially important to avoid washing food particles down drains because they, too, do not break down over time. Then there is the obvious one, hair, hair often sits in pipes, building up over time, so it is important to put in a filter or strainer that can catch the hair before it enters the drain system. And last of the five is bath salt, bath salts are extremely popular but many of these products do not dissolve, collecting in the drain over time and causing problems.