I want auto-embed of YouTube in blog posts, but not in tweets

I use the sharing feature of WordPress to send a tweet for each blog posting. That works fine, *HOWEVER*, the tweets contain autoembedded YouTube links. I don’t want that embed in the tweet, mostly because it takes up space from my 140-character limit. I’d rather people just come to my blog and watch the video there.

How can I easily remove the YouTube.com/watch/XXXXX embedded URL from appearing in the tweet? I can always go in and hack the PHP code, but if there’s an easier way, I’d love to hear it.

Thanks!

Reuven