Python the Dragon's Curve with turtle
Here are some suggestions and remarks, in no particular order:


i is not a great name for a variable in most cases, and especially not when it's not short for "index", as is the case in your draw_sequence function. I would suggest naming it direction.
The official Python PEP8 style guide states that class names should be CamelCased, so your class should be named DragonCurve, without the underscore.
There's no point in making self.seq an instance/member variable, since it's only used by the create_seq function and its value is reset on each call. It can safely be turned into a local variable.
Stick to using the LEFT/RIGHT constants instead of 'l'/'r'.
One small improvement that you could make is replacing your empty strings "" with a constant named EMPTY_SEQUENCE. This would completely hide the fact that sequences are represented as strings from the reader, and would make it easy for you to change the representation if you would ever want to.
Function names should be verbs, so opposite is not a good name for a function. Perhaps something like "flip" or "invert" would be more suitable.
The parameter named str will shadow the built-in function str. This is generally not a good idea, so maybe it should be named seq or sequence, since that is actually the abstraction that the function operates on.