As far as right and wrong is concerned, it is wrong as simple as that. What was your genuine aim to be with her? I suppose to make her contented as she was feeling depressed after knowing the fact about your brother’s age and what you are intent to do now, are two different things.
Her behavior clearly suggests that she wants to have sex with you but she might not be able to approach you in a straight line so being a woman she did what she could have done to instigate you. Now it is up to you what you want to do with her.
What I understand from your description is that you badly want to have sex with her but morally you do not have right to cheat your brother as it can tear down your relationship with your brother when you are caught. Therefore, if you are sure that you will not get caught then you may think of having sex with her. Chances are less for you to get caught but there are chances.
I would suggest you, refrain yourself but if you have decided to go ahead and would like to take a chance then when you find her alone in the home you may straight ask her for sex and I am sure from your description that she will not say no. You need to show some courage to get into her pants as being a woman she has been doing her best and impatiently waiting to widen her legs for you.
Best of luck and let us know the development.