I never do an on-line install of JAVA, I always download the off-line installation file.
You don't have to uninstall the old version of JAVA, from some time ago the JAVA update removed the old version.
What you most certainly 'have to do' is to close all browsers before running the JAVA update/installation, I have done that for a while now and the old JAVA plug-in isn't seen in firefox, see image. A search for npdeployJava.dll also reveals file not found, so it is removing that if it was present.
So I don't know why this is happening to you