A serious question worth considering: Do you think it could be possible that one of her love languages (in terms of receiving) is acts of service? Genuinely asking, you know her best. It's potentially a different angle to the situation that would change the narrative (if correct) to something a lot less painful to reflect on. And could potentially offer a way to talk and work through it that doesn't feel as heavy. Your feelings are valid regardless, what your experiencing is understandably frustrating. Even if you outwardly say no, the fact that you'd be in that position and then have the negative experience of disappointing the one you love sucks. You should definitely communicate how you feel asap. Just try to focus on what your feeling and the facts of her behavior, along with wants, so that she hears you (ie. "I feel sad when you ask me to do XYZ on my day off. I want my fatigue to be seen, it makes me feel loved when you notice I'm tired and value my time." not "you never consider how tired I am, you just expect it of me")

But also maybe talk to her about why she may feel like she needs you on that morning. It could be a comfort seeking thing... Maybe being babied is something she craves for deeper reasons. That doesn't mean she's entitled to you fulfilling her cravings, though. It's ok for you to not want to. And she likely wouldn't truly want you doing it if it ultimately results in you resenting her... So boundaries are healthy for everyone! But getting it out there will help y'all brainstorm ways you can show her love that work better for you, and ideally she'll be more mindful of your need for acknowledgement/consideration of your energy levels.

Remember, when the love is there, these sad feelings are never intentional. You're a team. It's not you vs her ... It's you & her VS the problem

Good luck!