WOW - Congrats!!!
I agree, try a baby gate at the laudry room door, they have small ones and the cat should be able to get in and out no problem.
As far a scratching and dry skin, the food probably has something to do with it. You are right that the brand she is on now is pure crap!! I would suggest getting Natural Balance - Duck and Potato. There are alot of people in the same boat as you and they all swear it has done wonders. And you can get it at Petco
I agree, I feel that all dogs should be on a heart worm pill. Good idea to get her checked out! I too apply Frontline Plus to manage fleas and ticks.
Shampoo and Conditioner, since she has sensitive skin, try Espree:
www.espree.com - they have all nature and sensitive types.
Best of Luck!