Higher bit rates, such as 75kbps, just means more information/less data compression. DTS is a higher bit rate because it uses less compression (vs. DD).
CDs are limited to a theoretical 22.05kHz and standard DD/DTS DVDs are limited to 24kHz.
Audio resolution is is the numer of bits (16, 24, etc.) This basically dictates the dynamic range and signal to noise ratio capability as well as the "preciseness" of each sample to the original analog signal. More bits = better.
I'm not that familiar with the bit rate displayed by the DVD player so I can't quickly speak to it's relationship to the sample rate although it would seem they would be directly related whereas a doubling of the sample rate should double the bit rate.
The DACs are at the mercy of whatever signal they receive when it comes to sample rate. They will default to whatever is coming from the player.
A higher number of bits (16,18,24) is not related to sample rate/sampling speed. It is related to bit rate (75kbps). So the difference you hear between DTS @ 75kbps and DD @ 45kbps has nothing to do with sample rate (which is always 48kHz) and everything to do with the bit rate which is higher because DTS uses less compression.
A video DVD (not including a 24bit/96khz type) will not produce anything over 24kHz whether it's standard pcm (actually 22.05khz), DTS or DD.
Even if you play a 24/96 disc your player may well output it at 48kHz. With this you would get the benefit of more bits (resolution) but not the higher sampling rate (HF extension).