You and your entire family have a lot to process. I hope you all find the emotional support you need.
If I were you, I would talk first with your aunt. Be there graciously for her. Ask to see your cousin if that's what your cousin wants. Try not to be offended if it isn't because there are a lot of feelings involved. Not just the ones that led to this event, but quite a few in the aftermath. It may be enough for your cousin and aunt to know you are concerned and supportive of the healing process.
As for your mother, acknowledge that she has complex emotions (without naming them) Then, tell her that this is a difficult time and your priority is focusing on healing. You can also tell her that your aunt may have chosen to wait on the advice of the doctor treating your cousin because it was what was best for your cousins mental health. Remind your mother that there are people she can talk to about her feelings butter you aren't her best option.
All the best to you and your family.