it all depends on who is on shift, how you are supported and how busy they are. I work at both hospitals and it all depends if you choose the Birth Center or Labour Ward. I have found from experience that labour wards at both hospitals are similar in approach and attitude that is sometimes less of woman centric as they tend to get very busy especially at C&W. However, the birthing centers are a different thing all together and provided you have a good understanding on what you would like to experience second time round, positive outcome can be achieved at both.
Remember that you can change hospital up to the point you are 36 weeks pregnant so I am hoping you have time but if you are having this feelings every time you come to do your antenatal meetings at Chelsea then probably change of scenery will help to remove bad memories. Kingston maternity unit is a standalone building neatly packed away from the rest of the hospital and many of my clients have found it easier to park and get to. Kingston also has an excellent pediatric unit. And of course, it is just not as busy as C&W. However, distance would need to be considered for the second birth as they tend to take less time with less preamble.
I am really sorry that your first birth have left this feeling for you and I would agree that an experienced doula may be an option to help and support you through the second journey. You can find a local doula through Find My Doula website or through search on DoulaUK. There are quite a few of us working locally so if you are interested I am sure you will be able to find the right one with the right skills for you.