I know what it is like to have a cr@ppy sleeper.
I'm sorry you aren't getting much support from family, it is really sh!t that no-one will take her for one night (who cares if she doesn't sleep, it is just one night of their life - they have the luxury of catching up on sleep the next night, unlike you).
You are doing a good job. Sleep deprivation is a form of torture and you are doing the best you can. It will get better, it doesn't feel like it now but i promise it will.