ETA: Oh my goodness, please do not pull your attention from her now, just to "get her used to it when the baby comes"! What a terrible concept in parenting! Alyssa can have whatever attention you can give her, and you can include her in SO many aspects of the baby's life too! Don't underestimate the amount of help she can be!
Congrats on the new baby coming!
I hear what you are saying, I really do. I hear you saying you need "me" time, and that you are spending a lot of time with Alyssa but can't entertain her all the time.
Here are my thoughts: First, she is getting up at 5 or 6 on the weekends, because, I'm assuming, that's about what time you get her up during the week to get her ready for daycare. If you want her to sleep in a bit (and there is no guarantee this will work), try moving her bedtime later and later over the course of a couple weeks until she is about an hour later than she is now. Maybe she will sleep in then.
Next, I know you feel that the best place for your daughter will be daycare for the summer when the baby comes. But, I feel strongly that your daughter would benefit GREATLY from being allowed to spend the majority of your maternity leave with you and her new sibling. I can see where maybe taking her to a babysitter (aka daycare) 2 days a week might afford you a nap or something, and I suppose that's fine. But her security with the changes and ability to bond with her sibling (and watch you bond) are important, and can't be captured from 6p-8p nightly. PLEASE consider keeping her with you during that time. It breaks my heart to know what you all will be missing as a family if you don't (I have 5 children, and work from home-no daycare used).
Don't feel like you need to entertain Alyssa all the time! I could probably do more than I do to play with my 3 year old, but you know what? Just my presence in the house, and my voice, and my smile are what he lights up with. He and I play several times a day. But being home with me is more than playing. We cook meals together, we shop together, he watches me care for his baby brother, he helps with laundry, chores, computer time. I do stop many times a day to have a 5-minute tea party, a tickle fest, or a book to read. We eat lunch together where we talk about his day, I answer questions, and I get to soak up his cuteness. Far to often, I forget how precious those moments are. But he will not forget. This is what is shaping him to be a young man. I am what is shaping him. He is learning my traditions, my thoughts, our family's way of doing things. How else are you supposed to pass things down to your children, but for spending the time doing with them, teaching them, coaching them? Don't miss that.