You could also choose a compressed video format. If the video is too long and too big, and quality isn't important, then you can make the video into a compressed video by using a compressed video format. This will allow you to send it over AOL even if it previously went over the size limit. If you're using a digital camera, then you should look in the user manual to find out as well if there is a way for you to take video with lower quality. This will of course mean that your videos will be smaller, but it will make them easier to distribute.
If you still can't get the file to send as an email attachment with AOL then you could try different email programs. Many different free email services exist out there and all of them have different size limits. If your video is too large no matter what you do then you could have a quick search through Facebook mail, Gmail and Yahoo mail, and see which one of them (or another) is able to provide you with the highest limit for sending videos.
Of course, a 1GB video is never going to be sent over email so you may have to consider other options. Instead of sending the video by email, you could always upload it to Youtube and then use the email to send the link to your friend. This works best if you don't mind other people seeing the video, but if you still want it to be private then you can make a list of family and friends on your Youtube account, and only they will be able to view it.