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And remember... she'll only be 3 once, and it'll be over before you know it.
ITA! Believe it or not, there is going to be a time that will happen all to soon where you'll miss all the 3-year-old adorableness and play time together

That said, 3 years is an exhausting age! (For us parents :D). And I'm not a fan of spending a lot of time playing if it's not some kind of play I really like

When my kids were little I dealt with situations like this by changing out everything - by distracting them completely enough they'd forget about what they wanted me to do that I didn't want to - does that make sense?
Soooo... my suggestion for the morning, after dad leaves for work, is to make that the time you and your dd get up and get out and go somewhere - it could be grocery shopping, to a park, whatever *you* feel like doing then. Entertain her, but on your terms

And even better if you can fit in a chore

Other tips in general at that age - she's almost old enough that playdates are going to help a little bit. There's still a lot of parental oversight needed at 3, but having a friend over will take a little bit of the "play with me mom" demand away. For at least a little while

Plus if you can find one friend that you can swap playdates with, that will give you some free time too when she's playdating at the other mom's house.
If you need to be at home, can't leave, can't find a buddy to play with, then have her help you do chores. My kids were oh so happy to "help" with laundry, sweep the floor, etc at 3.
Best wishes,
polarbear