Mary, correct painting is 90% prep work and 10% painting. Sounds like somebody forgot this when they painted the door the first time so it means a lot more work for you. Since there is Varnish on the door, the old paint is not sticking. You will have to sand it off, or at least in the areas where it is still attached and feather the edges in. Then wash with TSP, rinse, prime and paint. It will be a lot easier on you to do this if the door is flat. Knocking out a couple of pins and removing the handle hardware (2 screws) is not that big a deal and will make the work easier and allow a better job.