I personally took care of cleaning the house, and I always make sure to do so under the beds. I'm afraid if your daughter had trouble breathing, it might have been more because of the 44°C outside than the dust that accumulated over the couple of days you stayed there.
I'm sorry if the paint droplets on the stairs look like dust or sand but the house was recently painted and the stairs waxed. I'm sure given your professionnal background you'll appreciate the difficulty of getting rid of those !
As for the cleaning tax, I'm sure you'll appreciate the work it takes to clean a house this size, which is covered by part of the tax, while the rest of it goes towards replacing bedsheets such as the ones you left with black stains I haven't managed to get rid of.
The cleaning products are made available as per AirBnB policy, as are toilet paper, shampoo and soap on the grounds of these being the essential objects of the household.
Finally, I'd like to thank you for suggesting a toaster be put in the kitchen, which I have in the meantime.
Thank you for saying, and I wish you a good stay in Portugal!