I don't know about the playback cutting in and out, but if you are not using iTunes anymore, get it off your computer and re tag everything. Or, if you have the hard drive space, make a copy of your iTunes music folder, rename and tag everything, and don't allow iTunes access to it. Just use it for your other playback software.
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You're likely to get the best answer to this by posting your query to the JRiver user forum: http://yabb.jriver.com/interact/index.php It is a very active site with many knowledgeable users.
JRiver and iTunes do not play well together. They are really mutually exclusive, IME. You will need to point JRiver to the folder(s) where your media is stored. JRiver will then "watch" those folders, and import new additions into its library. JRiver won't move or rename your files - as iTunes will - the JRiver library is merely a database of what is contained in the "watched" folders.
iTunes has its own scheme for organizing files. I agree with Zd542: It's probably best to rename/retag your files. If at all possible, you can then then uninstall iTunes.
As for playback cutting in and out, I'd need more info about your install before I could even begin to help. JRiver has a logging tool that could will help resolve that.