Congratulations! I have to say, the 2nd doctor sounds a little... um... wacky? There have been many other threads on this topic - suggest you do a search of FlyerTalk on "travel while pregnant". If you are early on in your pregnancy, and there are no health issues, there should be no restriction with flying, and if you are farther along the concern becomes only if you might deliver.... I flew frequently with both my pregnancies (2 boys, now 18 months and 4 YO) up to about 5 months; many flight attendants fly until quite late in their pregnancies. Assuming your health is good, and you follow all the tips about staying hydrated, keeping blood circulating, eating right, etc., the biggest concern is probably your own comfort - my most miserable flying experience while pregnant was getting stuck overnight in a snowstorm at Narita en route home from Korea, very early on in the pregnancy (6W?) and dealing with nausea and hormones - but there was never any danger, or issue with my (or the baby's) health.
There is a specific type of compression stocking you need - my doctor recommended mine (sorry can't remember the details) and you can get them at a medical supply store or maternity store. Hawaii sounds great; below is a thread on Kauai while pregnant (I know, different island but possibly similar activities?). I didn't go to Maui while pregnant but just went in April and there is plenty of other stuff to do even if you don't feel up to Haleakala (I would use your judgment there - unless you're super-prone to altitude sickness I can't imagine an hour or two at 10k will do much, you'll spend more time in the plane cabin which is pressurized around the same!)
http://www.flyertalk.com/forum/hawai...-pregnant.html
Good luck and enjoy!