I am trying to update the IOS on my ipad and when I try to install it, it fails on the download saying I do not have enough storage space for it. I have 19.2G free on my ipad. Is it because my backups to the iCloud leave only 537M free on the iCloud?
Your storage in iCloud doesn't have an influence on storage space on the iPad. So iCloud is certainly not the reason for your issue.
If you can't update over the air (Settings - General - Software Update), connect your iPad to iTunes, and update it there. This will install a completely new version of the latest software on your device, and it usually needs less storage than the other method.