Or you could ask for a letter and not waive your right to read this particular letter before sending it out. If it is inappropriate, you could not send it. If it is fine, you could explain that you did not waive your right because there were personality conflicts in the research rotation but you still wanted to show your ability as a scientist.
If that is really not an option, I think it would be ok to just use other letters - likely you won't be asked, if you are you can explain (as politely and tersely as possible, eg "The PI had a different mentoring style from that which worked best for me so I moved to another laboratory.") Most programs want 3 letters as far as I recall, if you have 1 research and 2 professors who know you well, you will be fine.