i think you need a therapist who will politely refuse to tell your mother anything about what you talk to them about. and then, if your mother feels like she still needs family therapy to deal with this all, find another therapist to see together. for family therapy.
take care of your father, if that's what you think is the right thing to do. present as a man in front of him, if you think that will ease his mind, and it's more important for you to ease his mind than go 100% full-time.
your mother's problems are hers. tell her to see a therapist if she has that much on her mind, maybe she needs it even more than you. but you two can't see the same therapist for anything other than family therapy. it just won't work.
also, a therapist for mental problems, is a person that you talk to about everything. not just what's going on in your own little world, but everything that goes on outside and how that affects you as well. you need someone who can listen to you complain about how unfair your mother is, or how you hate having to present male, or whatever you think is great or awful, without giving you any advice. without telling you what you should do. your therapist may offer options, but must always leave the choice to you. he may help you consider consequences or analyse your reasons, but he can't tell you what to do.
it's your life, and you won't be able to deal with any mental problems before you start making your own choices out of your own will and for your own reasons. is it right for you to become the man of the house? aren't you becoming a stunningly beautiful woman? there are consequences to all decisions. consider your options and their possible consequences, think hard about it, and make a decision that you think will make you feel better about yourself. a decision that you can stand for, one that is your own and not influenced by other people's opinions.
other people can't see more of the future than you can do, and no matter what you choose, the outcome is likely to be outside anyone's predictions. nobody in the entire world has experienced exactly the situation you're going through right now. your mother and therapist are unlikely to have experienced anything even remotely similar, so why let their fears and prejudice influence your choice?
i have a stepfather who is sick. there's always been something wrong with him for almost all the years that i've known him. he could die from a stroke any day, but he chooses to live his life to its fullest and refuses to get chained to a chair by inactivity. i'm afraid it will hurt him if i transition, and he is the only one who's been like a parent to me. but in the end, i'll just have to do what i have to do, and pray that he is strong enough to handle it. but i can't take responsibility for his reaction, because that's something which is created in his mind.
family members burden each other with their problems, if we manage to share, we all grow stronger. but if it's one-sided, and one demands accommodation without accommodating the other, the relationship or the people will start breaking. i can't take all of my parents' problems, and my own, and carry all that alone. even if that's what they seem to expect me to do. i will have to deal with my own problems in some way before i can carry the whole load of my family, or i'll break.
can you carry the weight of both your family and yourself, make their burdens lighter by breaking yourself?
what if you can't bear it, and end up in the tragic end of statistics, wouldn't this just add to your parents' burden?
your family only think they need you to be a man for them. what if you do them better as a woman, being the person you were born to be?
and how many possible outcomes did your therapist consider before telling you to man up? did he consider you breaking? did he consider your family's sorrow if they lose you completely by denying you the right to be yourself? did he consider you as a well functioning woman with a steady job and enough energy left to take care of your father? did he even ask you how that would feel for you? whether you'd survive it?
sorry for the long post, i'm just worried about you and your family.
from your posts, none of you seem to be doing good with things as they are. something will have to change, and if you are the only one who are capable of changing, then the burden must be really heavy on you. but i think you also realize that a change is needed, and i hope you will make the choice that is right for you, and not what the people around you believe is the only obvious choice.