As an longtime owner of a DPF diesel I have the following thoughts about your question:
Both DPF and engine don't like cold idling (wear on the engine due to cold oil, acidic combustion byproducts and clogging, especially since a cold diesel engine produces lots of soot and your engine oil starts cleaning only when warm).
Since a diesel has a rather efficient combustion it won't warm up soon, so a mile isn't enough to get your engine up to operating temperature. In the makes I know the DPF will only start its cleaning cycle under some very defined parameters (the engine is up to temperature and is running above a certain speed for a certain time). A two mile trip and 5 minutes idling won't allow a filter regeneration.
The wear on the alternator by an additional start per day should be negligible, especially if you compare it with the cost of an clogged DPF/EGR or possible engine damage.
As long as you have prolonged trips under high load on most of your driving time you should not worry about the DPF. Yes, the DPF would prefer it to be hot the entire time, but 3-4 short trips per week with your driving profile (your comment to motosubatsu) won't do damage.
The 5 minute idling is contraproductive, both for your engine and surroundings.
It fills your engine and exhaust treatment with soot and acid from the bad combustion, won't contribute to filter regeneration and increases wear on your engine.