Aprezo.com

If the value of the U.S. dollar went up relative to other currencies during a recession in the United States, why would this be a bad thing for the U.S.? Also, how could the Federal Reserve work with another central bank to stop this appreciation? Why might these actions fail?

usually during a recession the dollar will depreciate because the demand for money declines.

If the US dollar went up relative to other currencies during a recession in the US, it would be bad for the US economy because as the US dollar appreciates, US exports are relatively expensive to other countries. as a result, NX will drop.

Y = C + I + G + NX
if NX drops, Y also drops.
output (Y) decreases, according a Okun’s Law, unemployment will rise.

The Federal Reserve can work with another central bank to stop this appreciation through foreign market operations.
the Fed can sell US dollars and buy other currencies to stop the appreciation. (selling US dollars will increase the supply of USD and buying other currencies will decrease the supply of other currencies. both actions will put downward pressure on the price of USD in the foreign exchange market.)

These actions might fail because other countries will have an advantage in their exports if the US dollar is relative strong, so they might not want the US dollars to depreciate. Another reason might be that some countries have fixed exchange rates against the US dollar.