Can you provide a bit more info on how you'd like this to work. Given that you're using parcluster, batch, etc., I suspect you're also familiar with parpool -- is that what you mean by running MATLAb in interactive mode? Would the following work?
c = parcluster('short');
p = parpool(c,28);
pctRunOnAll cd ~/DATA
forHpc runs locally, except when you hit parfor, spmd, etc. That code (e.g. parfor) will be run on the cluster and the workers will run in ~/DATA. Any code in forHpc that is not embedded within a parfor or spmd block, distributed array, will be run on your local machine.
Does this address what you're asking? You didn't mention if your local machine and the cluster share a mount disk. Is ~/DATA reachable from your local machine?