Side loading is a way to get apps on your phone that you cannot get from the market (ie z4root, wireless tether apps). It might work for getting youtube back on your phone.
Make sure you have a file manager app- I use astro as it makes side loading easy. Then either do a google search for youtube.apk or get the 4shared app from the market and download the youtube.apk.
Once you have downloaded the .apk to your phone go into settings>applications and make sure "unknown sources" is checked. Then go to your file manager app and under in your download folder find your youtube app and click on it. It should then give you (if your using astro) the option to open the app manager. Click that option and from there you should be able to install the app.