Yeah, that coop is way too small for 6 chickens. Especially 6 chickens that haven't been raised together since hatch. It would be like having to share a bedroom with your entire family, naturally conflict is bound to occur. Providing more space should help with the bullying and should be the first step. If you're still having problems with the older hen harassing others with more space then you would need to look at ways to disrupt the pecking order such as putting the bully in chicken jail.
Generally the recommended minimums are 4sq ft per bird in the coop, 1 foot of linear roost space per bird, and 10sq ft per bird in the run. If you can provide more that's even better.