Splitting hairs, but is the хорошо related to the плавать or to the умею?
From its position, it seems to relate to умею: I well know how to swim - which might be said in English when pointing out that you don't need swimming lessons, for example, because you know the theory of how to swim.
The point is that you know how to swim, but whether or not you can actually swim at all, never mind swim well, is a moot point.
This is exactly the sort of sentence that gives rise to the misunderstandings I get myself into with my slapdash Russian speaking, hence asking!
Умею implies having a practical skill, not just knowing how to do something in theory. So it is obvious that хорошо is related to плавать wherever you put it in the sentence. Я хорошо умею плавать = Я умею хорошо плавать = Я умею плавать хорошо = Я хорошо плаваю = I am good at swimming
I am not so sure that "I swim well" sounds natural in English (I'd rather say "I am a good swimmer"), but there is no doubt that, in Russian, "Я хорошо плаваю" sounds much better than "Я хорошо умею плавать". In fact, if someone says the latter, I would think the person is a foreigner.
Умею means "I know how to and actually can". Examples: я умею рисовать/петь/танцевать/читать/писать/кататься на коньках/ водить машину. Могу means "I can/may" in the sense "it is possible that I" or "I'll be able to" (the latter is more often translated as смогу). When talking about your temporary capability, you should use могу. Я могу к вам зайти сегодня (I can come and see you today). Only могу can be followed by a perfective verb. It is also used to talk about regained capability, e.g. Я снова могу петь (My voice came back to me, I can sing again)