I don't think you are being a brat. I think you are trying to work out where you are in this relationship and family.
Your DP spends 4 out of 7 days on his own, with only himself to think about (plus the stress of his job and travel)... On the face of it.. he enjoys this nomadic lifestyle and sees taking you and DD away as something good.. you see it as another chore that does not give you a break from the 24/6.5 of parenting responsibility.
He pays for childcare, contributes towards your housing costs and pays for trips away.
However your life is, there are always compromises, work, leisure time, family time, housing costs, disposable income, saving for the future.. it is challenging when you find yourself in an unplanned situation, without having grown together, had fantasy life chats, worked out what makes each person happy...
Both of you have had to make major changes to your lives, perhaps you see that he gets more of what males him haopy, than you do, maybe he sees that he is giving you what he thinks you need... time away from the hum drum of life, whereas what you crave is more time alone.
How would you like this to work? That he takes your daughter away for a few days on his own, that he stays in your house, works from home, looks after your daughter while you go away on your own, that he spends more time with the three of you as a family in your home, would you rather he had his own place and your DD split her time between you or maybe here is another option.
You are in a good postion, that your finances are stable and that your partner contributes to your joint life, that does not mean that your should put up with a situation that does not make you feel happy.
If he didn't work away... how do you picture ypur lives? More equal share of household tasks, breakfast and dinner together, shared nursery drop offs, one evening per week of personal hobby time, some individual time at the weekends each while the other person is with your daughter..
What would make you feel happier, acknowledging that life is not perfect? Would personal and then couples counselling help you to understand how to improve your life?
Have you talked to him about how you feel? How does he feel? What I don't get from your post is joy... life is too short not to have some joy and love... find a way to build that in.. then the humdrum / life load / difficult moments... take up less space and are less heavy.