Suggestions? Get a divorce. If you have 5 thousand to invest and want to build your own fortune behind your partners back, then do yourself a favor and get a divorce now. Your relationship is obviously not strong. I think investing is the least of your problem at this point. Sorry, but I would invest in your relationship now and build a nest egg together.
If you want non-taxable and untraceable then you probably want to go with things like precious metals and keep them in a safe deposit box.
To the best of my knowledge, any regular investment of that size is going to incur capital gains every year.
Call Merrill Lynch. Have them set you up an IRA. They can fix it so you have very little mail.