It doesn't sound like your hen has committed to being broody yet... my suggestion would be to remove the eggs for now (since they won't have developed right if they are only being sat on part of the time)... place golf balls or other 'fake eggs' in a nest area within the coop that you feel is suitable for a broody to set on once she does decide and begin a collection of eggs on a cool spot on your kitchen counter or somewhere else suitable for storage of hatching eggs. I just use a cardboard egg carton, place the eggs round side up, mark them with a date and when the carton is full pull the oldest eggs each day and replace them with the new ones (I only choose 2 or 3 of my best eggs each day). Tip one end of the carton up on a block about 1.5 inches and switch ends 2x day to help prevent the yolk from sticking to the inside of the shell.
Once your broody has committed (setting around the clock and only getting out for short breaks to eat, dust bath and poo, not laying eggs anymore and generally puffy and irritable looking) you can then give her whatever # of eggs you have chosen for her. Make sure they are marked at that time so you can remove any added later by other hens.
With your girls it shouldn't take too long before one (or both) of them decide to park themselves in a nest!
Good luck!
I wouldn't be surprised if the EE wasn't the one being sneaky! I have caught my broody hens (my silkie in particular) stealing eggs from other nests and carrying them to her preferred spot! They are incredibly resourceful when they want to be!
I'm thinking you will need to be finding her a few eggs in the near future!... or just wait, and she will find them for herself!