There is the possibility that either the dog or the other cat has somehow caused stress to the F1 while she is either using the litter box or has prevented her from using the litter box, particularly since you mentioned you have two alpha personalities in the house. It sounds as though the F1 is using displaced aggression toward the Manx. Having the dog intervene sounds like a recipe for disaster to me.
My F1 male prevented one of my F2s from getting to the litter box to the point he caused the F2 to develop chronic urinary disease which needed emergency care and surgery.
To fix the situation, I consulted an animal behaviorist who recommended more litter boxes, more individual play time and individual attention for each cat, addition of even more perches, and giving the F2 his own private space when needed. In addition I put the F1 on Prozac which led to a huge improvement in his aggressive attitude toward the F2.
Your F1 is telling you she is unhappy and the challenge for you is to figure out why and how to fix it. If we could read their minds, it would be much easier. You might try giving the F1 her own space for a few hours each day with a litter box, her own toys, water & food. I never leave my F2 out in the house when I'm not home. Either he or the F1 are put in a room away from each other when I'm gone. That way, I know there isn't any territorial issues happening when I'm not there to intervene.
I highly recommend doing a zoom consult with Marilyn Krieger, the cat coach, to get insight into and recommendation for resolving the problematic issue of two alpha personalities sharing a house.
https://www.thecatcoach.com/
Good luck and let us know how things progress.