Likely this problem relates to your WINE requiring libraries which also live under your /home/username file hierarchy.
If I required WINE for a project, I'd likely us Ubuntu + find a PPA which packaged the most current version of WINE. This way I could just install WINE anywhere + have it work.
That said, you can likely fix up your Library path as follows.
# Find all libraries in your WINE executable
# record all directories reported
# note: also run ldd on any non-system installed libraries
# add list of libraries to your ~/.bashrc or equivalent,
# listing every non standard path
Setting this in ~/.bashrc will work + may crash other programs.
Better to create a script... maybe... wine_start, which export LD_LIBRARY_PATH + then executes WINE. This way you can collect all these library path settings into a script, rather than polluting your default runtime environment.