OPs mother is retired so, assuming she's not involved in a high stress hobby that consumes 60-70 hours of her time per week, probably has time and energy to keep on top of housework most of the time. OPs situation is different.
OP I get it. Just speak to DD and explain you're really happy she's home, also a day early, your reaction was because of pure exhaustion. You'd counted on the extra time so you could have more energy and give her a nice welcome back and tidy up a little. You were so exhausted though that socially you were wiped out. You love her and really didn't want to argue, which you were worried would happen, because you were exhausted, so you went to your mum's to avoid that. You weren't trying to embarrass her, you basically just needed a hug and a bit of tv/sleep and then you'd be "human" again. Let her know she's ALWAYS welcome, but at the end of terms/half terms you'll be exhausted. And I'd add that she could have organised the take out without ordering you to do it.
She's not going to understand you 100%, but giving an open explanation, with some soft, loving bits in there, will go a long way to making sure this doesn't happen again. It'll also confirm she's welcome but you have boundaries. And if done kindly, should help repair whatever is damaged.
And to be very clear, that's an approach of trying your have open communication, love and also boundaries. I'd have been so bloody angry I myself may have said something I shouldn't! But the goal now is to clear the air and reset and lead by example.
If she orders you around again, I'd either give her short shrift, or turn it into a joke "Lol - sounds like you're looking for a maid, not a mother" and definitely not do whatever you've been told to.