"I just want to call the person who doesn't see my priority as valid and say 'yes, you don't understand what I am trying to do, at least respect it'."
Persephone,
I don't know what you want from whom.....but this may help with the general process of getting a priority met... First off, I have learned not to place my needs up for evaluation by assuming that someone has to "understand them" in order to honor a reasonable request. Understanding can become important as a general response to a person you are intimate with, but on a daily basis, I try NOT to explain myself as it diverts me into a territory that my N mom was lord and master of...fogging an issue with someone else's needs. A priority is just that...a priority and you don't have to present the person with a novel of information about why you have decided this is important to you.
What you are describing is all about energy. Ever watch that show "Dog Whisperer"? If not watch an episode. The man talks a lot about how animals perceive dominance and energy. He teaches people how to use their energy differently to stop an animal from bad behavior the minute the animal starts to think about doing it!!!. That was the task I had to engage in while overcoming my issues with priorities and other people. To me it is all about projecting rather than always "reading" the other person's energy. I had to learn to project an energy of priority.
I think that, just like the animals, our N's moved to shut us down the minute we projected even the "energy" of a priority. By the same token, we learned to perceive their priority energy in others and shut down the minute they appeared to want something different. I think we often go into situations with that old energy and feel we need to explain ourselves and ask for respect in order to overcome what we perceive as other people's lack of respect for us.
The way I look at it is that most people enter situations with priority energy. They know what they want and pursue it, especially if they don't feel any priority energy coming form the person. It is just like two dogs feeling each other out. I used to read their priority energy as a negation of what I wanted and collapse into a puddle of self-denial. It was the old feeling that I was dealing with someone who could not and would not see my needs. I was feeling them way more than they were feeling me and crumbling back into a "take care of me please persona". When the person didn't understand the contract I was making with them and persisted in going about their own needs, I perceived this as a negative reaction.
Judging yourself or the other person is waste of time when you want to achieve a priority. I find it helps to keep your mind focused solely on the goal and keep asking until you get it. Unless the person is an N, this will usually leave you feeling good, even if you don't get what you wanted from a particular person. Our mom's often fogged issues with numerous side arguments. When we become afraid that we can't have what we want, we are easily drawn off into making judgments that allow us to give up and blame either ourselves or the other person.
I began to realize that unlike my mother, other people were not mind readers and a weak presentation of my needs both verbally and energetically meant that it was seen as NOT a priority. I began to rehearse asking for things without second guessing what the other person didn't understand or assuming a lack of respect (which is what led me to feel angry and worthless). When they didn't hear me I simply repeated my NEED. I bumped it up to from a want to a NEED and let them know (without malice) that I was on a mission to get this need met. If they resisted I let them know I was leaving (without explaining or getting angry) to find it from someone else or better pursue my goal and I would see them later. Good people will assume that you will ask for what you need and go get it.