Planning a trip

We are planning a trip and will be gone for a week. We will be spending some of that week at an apartment (no known laundry machine), at a hotel (no known safe laundry machine) and at a family member's house (laundry friendly). The big question right now is, how many diaper covers do I bring? He tends to use 3-4 per day including the overnight times 6 days (sans laundry machine). I know I have enough disposable (biodegradable) inserts, the question is do we bring a suitcase devoted entirely to diapers? Do we trust the hotel's laundry? Do we allow the stink of used diapers to overwhelm our luggage? That's a lot to think about.