I don't see the problem. If you're at the Hotel das Cataratas you don't need transport to the Brazilian falls, that's the whole point of staying there. I would do the Brazilian falls the day you arrive. If you want taxis the hotel can undoubtedly arrange them, but I did not find the buses to be bumpy. You can take the park transport to the entrance and a bus from there to Argentina, which I would do on the second day, spending the whole day at the Argentina falls, and using the park transport there.

I agree with Thursdaysd's suggestions and would do the Brazilian side on your arrival day. The buses are fine, very regular and the roads are good so not at all bumpy. We found the Brazilan side to be very well organised so it didn't really matter much what time of day it was. On the Argentine side we got an early bus in order to be there as the gates opened and were glad we did as it got really busy (and hot!) later on. Most people jumped on the train and disembarked at the first stop but we stayed on until the very end and worked our way back. This worked pretty well as we got the first few observation points virtually to ourselves and the train was much less crowded on the way back.

You could negotiate a taxi for the journey but I don't think that is going to add a huge amount in terms of convenience. Our experiences of finding "honest" taxi drivers in SA were 50:50 at best!

Thanks for your replies. I had read that it is best to do the Brazilian side early in the morning before the crowds and we can't do that on the day we arrive. Well, we'll brace the crowds and do the Brazil side on arrival day.
Do you think its important to take a boat tour under Devil's Throat or is standing on the walkways adequate for appreciation?

Actually, there were plenty of crowds in the morning, but they disappeared at lunch time. I didn't take the boat rides and was very happy with the walkway. I did take a boat ride at Niagara (which pales besides Iguassu) and mostly just got wet.