You just sound like a really tired and stressed couple who're trying to find their way through the constantly changing and ever more complicated business of raising a child.
People say all sorts of rubbish in the heat of the moment. My DP and I have said vile things to each other when we have been sleep deprived, financially challenged, anxious about work, coping with illness, family interference, everyone else is doing it better than we are-itis :)
It all feels like that saying ' stop the world I want to get off' at times.
There is so much pressure to be 'perfect'.. And to get everything you think you need to do done in each day.
Actually you don't. So what if a 3 yo doesn't have shower? Or you have scrambled eggs for dinner and go to the park with her instead or just have a dance party in the living room to shake away your stresses and tire her out a bit - in a fun way where she gets attention without it being about getting through to the next bit on the routine.
And that's another thing. People take the word routine too literally. Yes children thrive with structure. But structure can be as basic as ... Breakfast, lunch and dinner and bed.
So much pressure is self inflicted. Try to relax a bit. Careers are important but your marriage and child are more so. And that works both ways. It's not just about you compromising ... Your DH needs to as well.
So no your marriage does not need to be over. You and DH need a little break ( doesn't have to be anything more than planning to have a lazy weekend...pretend you've gone away so you don't see any friends, no clubs, no shopping no nothing that you usually would do). Take DD out. To something where you don't have to interact with others unless you want to... A play park, national trust, the seaside( Maybe not during these storms) but somewhere the three of you can spend time just 'being' together. And while she runs, skips and plays .. You and DH talk.
About the joys of your DD, what you live about each other, happy plans for the future, more DC etc. frame it all in the positive. And together decide what you're going to stop doing, the things round the edges that aren't really, really important.
You can get through this. In the next couple of years DD will be at school and it will be all change again.