Connection of the washer drain hose to the tub drain is very important. This will help prevent leaks for example.
There should be a drain valve where you can hook up a hose and then open the valve to drain.
Suck it out with a piece of garden hose or a piece of tubing
Sounds like a venting problem. The washer is trying to push the water down the drain and the tub is an easier route. When it stops pumping, the washer drain become the vent and lets the air escape. You can try some drain cleaner in the tub and the washer drains. This may open it enough to help.
You have to use toilet more
The main line drain is clogged or septic yank needs clean out.
The drain from the toilet to the main or the main itself is partially clogged or collapsed. There is probably enough room for the sink to drain but the washer puts out so much water all at once it can't get through and backs up into the tub and toilet.
The best way to drain a hot tub is to use a pool vac hose. You just simply need to get the syphon started using the jet and the tub will be drained quickly. http://www.whatsthebest-hottub.com/forum/index.php?topic=10930.0;wap2
You can run your discharge pipe from the washer into a laundry tub with the drain put in. After the wash cycle, the water will discharge from the washer into the laundry tub. Keep the water in there and replace the washer discharge pipe back into the usual drain. Let the washer run it's normal cycle. Take the clothes out and put them in the dryer or on the clothes line. The next step is the tricky part. You have to get a pump of some sort to put the discharged soapy water from the laundry tub back into the washer. This water will still be okay to wash the next set of clothes. I would wash the whites first, though. lol
It goes into the main sewer system. It will go through your sewer system and then out to the main sewer. That is if you live in town!
If you have slip compression fittings (brass/PVC) on your bath tub over flow and drain then you need to have a adapter PVC glue to compression before the trap running vertical and you will also need a access to inspect the compression fittings by most codes. I use glued fittings on all my tub drain and overflows because its the best kind of connection and you don't need access to it.
The tub and toilet connect to the same drain at some point. The main drain was plugged but the connection between the toilet and tub was still open. Water seeks it's own level. When the water came up in the toilet, the tub was lower so some of it went there.
Once the old tub gets into the drain it is impossible to remove.........