Well in my playthrough it should be clear to Chris that I actually enjoy her to be dominant. Would be really weird for my char, if she would want to be equals just because my character is competent and trustworthy otherwise. Hmm probably would tell her: Alright, give me the key. I will try my luck with Dr. Walker then.
Also want to add that not every dominant woman just looks for an even more dominant man to break her in. Imho being dominant, submissive or a switch is similar to being hetero, bi or gay. Meaning it's something you have a clear natural disposition for and if you are mentally stable you don't simply change that to fit another person's preference, no matter how much you like them.