I have a bunny that really despises it when I put my hands in his cage too. While spaying can definitely help, you can also help her be a little less territorial and a little bit more trusting. I think that you can definitely help that with some trust building activites, for example sitting on the floor with your bunny and just letting her come up and sniff you and get to know you. Also, hand feeding treats at a regular time, for example before work or when you get home, will help your bunny get excited about you putting your hands in her cage to give a treat!
All my bunnies really hate being picked up, so it may also be that she is scared that you are going to pick her up each time you put your hands into her cage. For awhile, try to not pick her up too much unless it is necessary, and maybe she will feel better about you putting your hands in her cage
The territorial poops can also be triggered by other scents – is there another bunny or animal that is in “her” territory that she might be marking her territory against?