Well, here is a link to a comparison chart of popular online storage services:
Keep in mind that uploading a 4gig file is going to take Time, no matter how you choose to do it. Do you know what your upload speed is? If so, do the math and see how long it’s going to take. If you choose to go this route it’s better to start the upload before you go to bed and let it run all night.
I still believe the post is a better option, but that is entirely up to you.
Another thing you might want to consider is converting the video to avi format, something like DivX. If your daughter has a stand alone DVD player, perhaps it can handle DivX, check the specs. If she’ll be watching on a computer, then she needs nothing else.