As for your question, first the unemployment rate is a bad measure of the strength (weakness) of the economy. When people stop searching for jobs for instance, the rate will fall. But that is not exactly a measure of economic strength, or a good signal to the fed to push rates up or down, is it? Look at the labor force participation rate instead. It gives you the proportion of employed people to the total labor force pool (i.e. excluding retired, disabled and people in school). It is more than 4 percentage points below its all time high (which was smack in the middle of the Clinton admin, btw).
So the Fed pretty much did all that it could do to raise inflation expectations (i.e. lowering short term rates and buying longer dated bonds) by the trillions. And yet the inflation rate hasn't budged, hardly at all (notice that most of the volatility of the CPI is in food and energy and you have to be kidding if you think the Fed can drive this...even then we haven't hit 4% in FOUR YEARS. Given that wages are by far the biggest cost input, I don't see how anyone would expect inflation until LFPR goes way up. So yes, there is a relationship, and right now it would take a huge change in employment (do the math on 4% of able bodied 18-65 yo's in the US today) to even start to push on inflation. In normal times, there is a definate relationship. Of course, that relationship can (and does) break down on the other side too. You can't just generate huge amounts of inflation to continually improve employment either.
So there is a relationship, but lets say that the relationship has multiple equilibria. We've had trillion dollar deficits and have been printing money by the trillions and yet there is almost no change in inflation, in four years man. This suggest that we are in a hugely depressed economy and as stated above, gold buggery would have likely plunged us into 20-30% unemployment (i.e. Great Depression II).