I am in the process of changing PhD programs, and my previous supervisor cannot write a letter that is purely positive. The main difficulty is that she wants to include details about what happened at my previous university; however, we do not agree on all these details, and she seems to be unwilling to debate the past. She believes that I should (or I may have to) explain myself and that I can't justify everything I have done in my previous institution.
Other faculty members I have talked to are of the opinion that if I have to explain myself like this then it is not a recommendation letter anymore and recommend not asking her for a reference. This is difficult because I can get other letters, but the strongest letter that I got was from my first supervisor, and I expect the other ones to be good but not stellar.