Ideally I would like to live in Poland, work from home and travel across the EU conducting these trainings, but I am not sure if such a thing is possible on my Spouse or Residency permit.
In a nutshell - yes, you can do this in any Schengen country. There may be an issue with Germany and Austria (the last two countries to uphold restrictions against Poles) - but no-one is really going to care less if you're turning up, giving a training session and leaving again. These issues are also null and void as of 1st May 2011, when all restrictions against Polish workers will end in Europe.
Just make sure that you declare the income to the Polish authorities :) You could be surprised at the powers that the Polish tax authorities have... You may also have to formally register as a business - depends how the Americans pay you.
But be warned - you need to make sure that you have the residence card in hand before travelling. The visa won't be enough, unless you're entitled to the 90 day Schengen tourist stamp.