without knowing what code you are using on your button and how you have it formated etc, i would say i think the script that you are running is holding up RR from properly embeding IE (timeing). I would try to format the code so it loads IE and embeds it first, then.. execute your script and let it do its thing. Only issue you may have with this order is IE will display a 403 until your connecton is active, and if that annoys you (it would annoy me) you can create a generic web page thats not so ugly as the 403 and set that as your homepage.
There is also a place i believe to have RR execute things when it comes out of hybernation/standy (not sure 100% as i never use these states)
as for your second issue, you can use the click hold feature on any button and have it set to execute your script. The way the click hold feature works;
This is my play button in my skin
click it normally and it functions as a normal play/pause button
click and hold for 2sec and it mutes the audio.
instead of placeing your commands inside quotes, you place them inside the @ symbol, and in RRSkineditor the code goes into the tooltip box. Really easy to do, if you copy and past the above code into a skin and look at it in the skineditor, you will get it instantly.