I'm pretty easy going when it comes to traditions. If dollar dances have been practiced in your family for generations, I say go for it. It would definitely be considered a faux pas in mine, though, and I'm not comfortable with it.
However, I was reading on some other boards about a bride who's granny went to Ireland and bought her an Irish dance bag. I had never heard of this being specifically an Irish tradition (though giving money to the bride and groom during the reception is a tradition in a LOT of cultures). But interestingly enough, I found a cute little "bride's pocket" online. Made from a Irish crochet pattern, circa 1910. Cool, eh?http://www.paris1900.com/Vintage-images_A4.html