Use both differencing and normalization in time series modeling to make it stationary?
Normalization does not stationarize a time series, as by definition, a non-stationary process has time-variant unconditional joint probability distributions - this implies that the mean and variance changes over time. 

To see this for yourself, try computing the mean and standard deviation then normalizing the first half of the time series. Keep these estimates and transform the remaining half, and the resulting time series is still non-stationary.

Differencing $K$ times is a common method of stationarizing time series if it is integrated of order K, $I(K)$, and usually works in practice. However, note that stationarity implies $I(0)$ but the converse is not necessarily true.