Sudden cat stress problem.

We moved to a new home at the beginning of July and our cats had a litter tray plus access to the outside via the back door. We got an electronic cat flap put in the back door and weaned them off the tray so they could go outside when they wanted and all's been mostly fine. Our very nervous Amber got used to it in no time although the other two females were still a bit hesitant. Yesterday one of them weed on the carpet by the front door - something she has never done since we got her several years ago, and today she poohed on the inside doormat by the back door. On the odd occasion my OH has seen a large black cat around, but Amber and our other cat haven't had any indoor accidents. It's just happened all of a sudden and I don't know why and what to do for the best.

It sounds like a stress reaction to the threat of another cat to me as well. Your cat may feel unsafe to venture out to do her business but most likely the position by the entrance is a message marker 'this is my territory'. Cats live in a world where scent is very important and they use it to define boundaries and conditions. Subtle scents from head rubs, stronger from marking by spraying and the ultimate billboard of dung.
Always worth keeping an eye on who is doing it in case it is a physical health problem.
You can get pheromones like Feliway that may help or supplements like Zylkene. Moggy valium.