Typically this is press fit installed with a fixture at the factory. It would be a good idea to freeze the new part prior to installing it to aid in the installation.
Some dry ice around the one in the final drive might help to get it out. Take a paper or plastic cup and cut a hole the size of the breather in the bottom, tape over the hole in the top of the breather, (since you presumably broke the whole top off before), so nothing gets in the diff, place the cup over the existing breather and fill the cup with dry ice. Wait a good 20-30 minutes, adding more dry ice as needed, then go after it with the vice grips after some taps with a hammer from different angles. Hopefully it will pop out w/o too much fuss.
At the same time you're cooling down the old one, use some dry ice to freeze the new one too. It will shrink it slightly, making it easier to install and when it warms up it should be a tight fit. You may still need to use a hammer to seat it in the final drive, but be gentle to avoid breaking the new part. I would also heat up that area of the final drive with a propane torch or heat gun before installing the new frozen part.