I think it's appropriate to attribute some grumpiness or moodiness to bereavement and give someone a bit of the benefit of the doubt and patience as they deal with a difficult time.
However, that does not extend to everything and certainly is not a reason for you to work in unproductive conditions. From your side of the story, your supervisor seems misguided as to what makes for productive working conditions. She also sounds a bit erratic in terms of shifting feedback and expectations. It's possible the solutions she is proposing are solutions that would work for her, or have worked for a past student, even if they do not work for you.
Disability Services may be useful, but I would start by asking them for advice about how to approach the situation rather than to enforce some accommodations. I think it would be far better to come to an understanding with your advisor directly about what you need to be successful. The accommodations you are asking for do not sound to me like they are particularly unique to any disability or condition (even if that may be a valid and convincing argument for them), these are things that fit quite reasonably into general variation in preferred working habits.
Unfortunately, there is no magic formula for interacting with people to get what you want or need from them, and certainly no formula to do so without offending anyone. Personalities differ, and general guidelines that work with most people might not work with your supervisor.
My general advice would be to have a conversation starting with your shared goals for your project and to try to come up with a shared understanding of a reasonable timeline, and then move to discussing a plan to get there. I would ask specifically why her preferences for working hours are what they are, and start from those reasons when making an argument for why you think a different structure would suit you better. You could request a trial period, where you've agreed on some progress to be made by some specific time, to show that you are able to make that progress under the conditions you propose.
Another tip I commonly give here is to suggest you bring up the problem you want to solve rather than your solution. That is, start with "When it's noisy I am not able to get work done" rather than "I don't want to work in the office". This lets people feel helpful by coming up with solutions for you, rather than feeling like you're defying their own preferences.
Of course, your advisor may be entirely unreasonable about all of this and insist on a particular way forward that doesn't work for you. In that case, maybe you want disability services to impose some accommodations for your work environment. However, I do not think a supervisor/student relationship works well when it is adversarial. Mentors must be invested in their students' success; these are battles you should be fighting on the same side of. That doesn't mean there can't be disagreement or conflict, but rather that the end goals should be shared. If your mentor needs to be forced by some third party to support you, that would suggest you are not actually on the same side. If you cannot come to some agreement with this professor about working conditions that suit you, I would strongly suggest you consider finding an alternative mentor.