That's a tough one to answer. Allot would depend on the chinchilla, it's age and IF it is willing or even able to get use to this particular 'routine'.
Chinchillas love a regular routine. IF the chin is young and this would be a regular routine, it might be able to adapt.
Normally, I do not suggest such a thing, but, a 45 minute drive is really not to bad ... if it is a consistant routine and the chin does not get car sick. We have had chins that will ride on my husband's shoulder for over 100 miles and seem to love it, while others just want to hide in a quiet dark place and not be bothered.
At the same time, you also have to consider what would happen to the chin should your car break down. Do you have a way to keep it warm in the winter (a blanket and 'canned heat') and cool in the summer (a cooler filled with ice) for however long it might take ... should your car break down? There's lots of things to have to consider.
A setup at the dorm and a setup at home ... as close to the same as possible ... this includes temperature, number of people, food and routine.
Now, for the real bummer ... What if you get a chin and it can not adapt to the routine? What do you do then? I feel chinchillas should never have to have more than 3 homes in their life time ... (1) the breeder ... (2) the first "owner" ... (3) the second "owner" ... I don't even like the idea of a 2nd owner ... I prefer a chin go back to the original breeder to become a permanent resident there. Chinchillas are not just "pets" ... with their long life expetancy they must be considered 'part of the family'. (I know one girl that kicked her boyfriend out to be able to keep her chin.
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Just some things to consider.
Jo Ann