To what extent is acceleration relative? I realize there are answers to my question many places across the internet and many places on this site, but from what I have seen, most of them either involve terms I don't know or assume you can use a test mass or "accelerometer," which I think does not apply in the case I outline below (if it does, please explain how the accelerometer would work). After what I deemed enough time trying to understand various internet explanations, I decided to ask my own question. Please answer the question in a manner that satisfies the situation below, and please refrain from references to equations or devices that I, someone who has only taken a year or two of physics, would not be well acquainted with.
Situation: Someone is in a closed lab in which every particle, including those that make up the lab, experiences the same constant force. (I don't believe it is necessary to articulate exactly what is causing that force, but if it is please explain why.)
To clarify: I am looking for a conceptual explanation about the extent to which acceleration is relative. It seems to me that, in the situation above, there is no way to tell if you are accelerating, but I keep reading that the acceleration of a mass is not relative. 
My problem with the answers I have seen is that they often don't speak in terms I understand, and when they do they are often unsatisfying or contradict other answers.
For example, in this question: Is acceleration relative? 
The first answer doesn't explain what is wrong with viewing an accelerating reference frame.
The second answer is close to what I am looking for, but seems to disagree with everything else I have seen, and simply mentions the idea of "all the mass in the universe" without explaining why that matters.
The third seems to take it as a fundamental assumption from Newton's laws. To me this is unsatisfying. It seems to apply that, for any object, there is some real acceleration, but there may be no way of finding that acceleration. Basically, the argument seems purely platonic. I would hope that an unsupported assumption isn't all there is to the answer.
An example of an answer I don't understand is the first answer for this question: Why acceleration is not relative in General Relativity? 
The answer talks about local experiments, which I don't think would work in the situation above, then goes on to talk about Minkowski metrics, which are completely foreign to me.
 A: Your example situation does not make sense. If every particle in the lab experiences the same force then every particle will accelerate at a different rate depending on its mass. The lab will be torn apart.
Neglecting that example, velocity is relative to the frame of reference. It is the same in all frames which are at rest relative to each other. 
In the same way acceleration is relative to the frame of reference. It is the same in all frames which move with constant velocity relative to each other (which includes being at rest). 
We could extend this to 'jerk', the rate of change of acceleration, and all higher derivatives of position. 'Jerk' is the same in all frames of reference which move with constant acceleration relative to each other. 


It seems to me that, in the situation above, there is no way to tell if you are accelerating, but I keep reading that the acceleration of a mass is not relative.

Your example scenario seems to be asking if it is possible (in a closed, window-less laboratory) to distinguish between uniform acceleration in empty space and being at rest in a gravitational field. This is Einstein's Principle of Equivalence. The answer is No, that is not possible. Those two motions are equivalent. Likewise it is not possible to distinguish between free-fall acceleration in a gravitational field and zero acceleration in empty space. 
However, it is possible to distinguish between two different magnitudes of acceleration in empty space, or being at rest in two different magnitudes of gravity. As Ben Crowell explains in a comment to Why acceleration is not relative in General Relativity?

what GR says is detectable is acceleration relative to a free-falling frame of reference.

