"It sounds like you're hurt that I have some energy for my brother but you don't see me having energy for you on a Friday night. You are right, we often just stay in on Fridays, and I'm very often exhausted. How about we plan some Fridays out soon?"
The likelihood of me getting that whole paragraph out is very slim. Maybe something shorter like: "it makes sense to feel jealous when you see me having more energy for my brother than for you. I would probably feel that way too."
the most compelling way to validate someone is to be sincere, and to do it authentically. are either of those examples of how you normally speak to her? they sound, to me, scripted.
She says: "I'm jealous."
tone and context are very important to consider. for instance, a lot of people make this sort of statement innocuously, to more or less mean "wow that sounds fun". you were talking about just having drinks with your brother, so ill assume thats not what she meant, but then again, be careful not to validate the valid by giving it more credence than necessary.
How about we plan some Fridays out soon?"
i think you were on the right track with some variation of this. this
is validation. it says "i care about how you feel, and im interested in addressing your concerns" without saying "i care about how you feel, and im interested in addressing your concerns".
shes saying she wants more time with you. in a personalized way, acknowledge it, and give her your best version of that.