Hi, OP -
I am a former Russell Group admissions tutor who has sat on many Mitigating Circumstances panels and while I think prospects are basically good, it isn’t necessarily going to be in the way that you expect. I am going to start by tagging @GoodThinkingMax, as she is also an academic with a lot of experience in this area.
I think your DC’s best bet by far is to apply to restart Y1. Even if they pass this year, their foundations in the subject will be shaky. Y2 is generally a big step up from Y1. Your DC is liable to anxiety and stress. Student Finance will allow this. Why would they not give themselves the best possible chance to succeed? This is a pretty common situation. Ideally the letter of reference, not the PS, should explain what happened and express a belief in the student.
Max and I know that the most common mistake students make, by far, is to compound their errors. Typically this is in the area of MH. They start by needing a few extensions for stress, before you know it they are spending their summers preparing for resits. If they are lucky these have been granted as first attempts, but that brings its own pressure. They limp along in this way until they either fail outright or achieve a lower degree classification than they could have if healthy. And they have been miserable. Starting anew on a shaky foundation seems a bad idea.
Creating a strong foundation is the key to avoiding this. In a couple of recent threads Max and I have advocated for time out. You’ve given no indication that your DC needs that although if you have concerns, Health First is definitely the way to go. And if it will take a year to get DC into a programme they are happy with, that’s fine also.
I am not sure whether retaking ALevels after a year of uni might help? Because of DC’s circumstances, if I were applying for next year and didn’t have the grades, I would contact admissions about this. (BTW such enquiries are always better received coming from the student than from their parent.)
Finally, separate from the DSA, each uni has an Office for Students with Disabilities, maybe by a different name. Some are reluctant to sign up with it. To sign up and use any help you are entitled to just levels the playing field and there are other advantages I won’t go into here. Best wishes