I would hope that at some point you and the other PM can work this out, but I was able to find this out on the help areas:
"We have a saying at WikiTree: Privacy controls are for privacy, not control. Privacy Levels and Trusted Lists enable you to collaborate while preserving necessary family privacy. They're not intended to enable certain family members to own and control the family history."
And also, in the section on "Management of Modern Profiles":
"Even here, the Profile Manager should not think of themselves as the owner of a profile. They're more like a steward or curator. They lead the family collaboration. They have a responsibility to share the profile with other family members. If they don't want this responsibility, they should let another family member be the Profile Manager."
However, with all this being said, the goal is not to brow beat another family member into surrendering control of a profile, but to (hopefully) respectfully ask for permission to help each other grow the family tree by collaborating to improve on the single profile. From what I can tell of the couple of public messages, it does appear that you have asked nicely to be involved in this profile, but without understanding the reasons why someone would be reluctant to allow another family member to help out, I can't speculate further.
I would try to strike up a private conversation with the other profile manager and ask if she would share her concerns with you over this profile, and explain your reasons for wanting to collaborate on efforts. Hopefully the two of you can work out how you can both help to make this profile better.
If for some reason you become overly frustrated with this issue, I'd recommend following this protocol:
See question #4 which seems most applicable to this particular situation.
Hopefully this helps.