Glad you got it working. The output should be the same. Perhaps you're still running your local quota command?
What I was trying to nudge you towards was that using back ticks on the quota command is executing it against your local machine and storing the result in the variable. Then later you were trying to send the result of the local quota command to the cluster over ssh. You probably also discovered you need quotes around the IP, and the case structure doesn't look right. you probably want a for/in/do structure there instead if you plan to have a list of targets to run it against at some point down the road.
If this post resolved your issue, help others by selecting ACCEPT AS SOLUTION or adding a KUDO.
I'm with Sean - there shouldn't be any difference between running a command via SSH or via a direct login to the CLI. I use SSH (well, Plink from Windows) for tons of scripted stuff where a command line is just convenient.
Another suggestion for improvement - use "rows 0" rather than "rows 99". Setting rows to 99 can still paginate if enough data, while rows 0 will not.
And since you mention this has to come from a UNIX box - just have to ask - how's your perl? If you have decent perl skills, there are additional options to get just the data you need and format as desired using the NMSDK alongside perl in functionally small scripts and you don't need to worry about setting options and such to get the data. Just a thought for your consideration.