Is it true that fiscal policy is most effective when the demand for money and the demand for investment are both sensitive to the interest rate?
This statement is not really true. Fiscal policy will be most effective when the demand for investment (the IS curve in an IS/LM model) is sensitive to interest rates but the demand for money (LM curve) is not.
Fiscal policy would have its greatest impact if the LM curve were horizontal. This would mean that demand for money was not related to the interest rate. In such a case, a fiscal stimulus would cause only an increase in real GDP (and no increase in the price level). This would be the best possible impact of a fiscal stimulus.
However, if IS curve is vertical (if there is no connection between interest rate and demand for investment) fiscal stimuls will not work. An increase in LM will lead only to inflation and not to any increase in real GDP.
So, the statement is half true. You need the demand for investment to be sensitive to the interest rate, but it's best if the demand for money is not.