Problem one: rough idle only when warm

Problem one: rough idle only when warm. When I first start my car it does perfect. After I drive for about 10 minutes when I stop it idles very rough and loud. As soon as I touch the gas it completely goes away.

Problem two: for the past two weeks I have noticed my transmission taking slightly longer to switch between first and second and second to third gear. I have an automatic transmission. Typically it shifts around 2300 rmp, now it is shifting closer to 2700 rmp. My husband says it sounds like it is slipping when at the 2700 rmp and about to change gears. I think it is just the sound of higher rmp. I do not have any change in gas mileage or driving. It pulls hills the same as always. I took it to a transmission shop today, and of course, I was told I need a new one. Is there anything else that could cause this problem?