It sounds like you may be mistaken as to how this is wired, or that perhaps I'm just not understanding your explanation. As others have mentioned, it's not possible to get 240 volts from a single pole in a 120/240V split phase system. Each tandem breaker provides 2 120 V circuits, this is true. However, if you measure between the terminals on a single tandem breaker, you'll get 0 volts. This is because the terminals are both powered from the same leg, and so are at the same voltage potential. If you measure from a terminal on the top tandem breaker to a terminal on the bottom one, then you'll measure 240 volts. This is because each breaker is connected to a different leg, which are each one half of a 240 volt circuit.
With all that said. For this setup to work, one appliance would have to be connected to both breaker. Something like this...
Notice that each appliance circuit has one wire connected to each of the tandem breakers. In this situation, you'd need a device like Speedy Petey shows.
Which ties the breaker handles together, to provide common trip characteristics.
Notice how the inner handles are tied together, and that the outer handles are also tied to each other. This way if either trip (or are turned off by the user), the entire circuit is shut off.
If this is wired the way you've explained, where the dryer is connected to the top tandem and the heater is connected to the bottom. Then there's some magic going on in those breakers.
Depends on how much load the rest of the house is putting on the service at the same time... but if the total demand stays under what your service is rated for, and you use wiring that can handle the 50A demand, you theoretically should be OK.
Run the numbers.
(My electric drier plugs into a 220V outlet fed by a pair of 30A breakers, and I have only 100A total service; that's roughly proportional to what you want to do. When I switch to a gas drier, I'm planning to re-route those 30A legs to my workshop.)
Best Answer
Yes you can swap breakers out, but take extreme care to match wire to breaker. Don't use 14 gauge (generally white) wires for a 20 amp circuit. Also note that most 220V circuits in the USA require a tandem breaker taking two slots.
Investing in an electrical permit is highly recommended, if your jurisdiction will inspect at the end of the job.