Can someone please clarify this for me. When I choose to go on a side quest does it go on top of the current quest? So that I don't need to worry about the negative side effects of the previous quest card until the side quest is complete?

Nope. Most quest effects still trigger regardless of how many quest stages are in play or which you have chosen to be the current quest. Certain keywords like Siege, Battle or Defense however will only have effect if the quest stage with that keyword is the current quest that round. Similarly any quest stage that has text along the lines of "whilst X is the current quest do x" will only take effect if you choose that quest card to be the current quest for the turn during the quest phase.

Thank you for the clarification! If it makes the game harder it must be true =) I'll start placing my side quest above the main quest when it is active instead of on top.