Okay so this argument is not entirely logical, but I'll explain why after addressing some points in your post.
Your 2 year old child needs a blood transfusion immediately but the only person around that can do it in time is the mother because she happens to have the same rare blood type.
She doesn't, actually. For a moment you had me really worried, but then I remembered I don't have a two year old daughter.
Sarcastic humor aside, I am assuming you would like me to imagine your scenario, so I have. It is quite a sad scenario, I would never wish it upon anyone.
Due to bodily autonomy, in no way is the mother morally or legally obligated to give her child her blood in order for the child to survive
Well hold on there. You are right, in that a mother is in no way legally obligated to giver her child her blood. I am completely 100% on board with you.
The morality is not as simple as you would like to make it seem. If you have the opportunity to save a human beings life and choose not to, is that moral? If you saw a man clutch his chest, scream, and fall to the ground would you call 911? If you didn't call 911, would that be immoral? I would argue yes, it is immoral to let that man die if you have the capacity to save them. Even if you are running late to a meeting or something, if you are the only person around and you do not do something to try and help that man, I believe it is immoral.
So back to your example, of the matter is a blood transfusion and the mother chooses not let her blood be used to for let's say religious reasons, I would definitely call that immoral. The amount of blood a baby would require in a transfusion poses no health risks to the mother.
If it was my child I would feel 100% morally obligated by my own system of morals to give my child my blood.
same for an organ
For an organ, yes, we agree that the mother is not legally obligated to give her child her blood.
Morally, this again cannot just be stated like it's black and white.
If it was my child, and it needed a skin graft, or part of my liver, or a kidney, I would feel a moral obligation to try and help it survive.
I am not saying that it is immoral to not help the child. It is immoral to not at least consider the options to help it survive.
or anything else of her self that her child may need to live
This statement just became false. The woman is definitely obligated to give parts of herself to the child. She is responsible both legally and financially for making sure the child is fed, clothed, bathed, educated and a whole slew of other things. We aren't even talking moral obligations, I'm talking legal ones too.
For this reason abortion should be kept legal.
Uuuuuuh what
I grant the same 100% rights a 1 second old fetus gets compared to that of a 2 year old child. But a woman's bodily autonomy is greater than the needs or wants of her child
This is fallacious reasoning. It presupposes the existence of that woman's 2 year old child. That child didn't poof into existence in your imagined scenario. It was fertilized and gestated inside of the mother's womb whether the mother liked that fact or not. That child in your imaginary scenario already went through 9 months and then 2 years of forcing that woman to sustain it with energy and sustenance.
For this reason abortion should be safe, legal, and rare.
It is not for this reason. I do, however, agree with you that abortion should be safe, legal, and rare.