For two people supposedly in love, you certainly rub each other the wrong way. Grouse and bicker, grouse and bicker -- you sound like ill-tempered siblings, not like lovers at all. You can't seem to make things run smoothly no matter how hard you try.
There are misunderstandings galore; you zig when your partner zags, your lover wants time together at a time when you're craving solitude. And the impatience and frustration you both feel with each other isn't making anything any easier. Why is it that you seem to blurt out the absolutely worst thing to say at exactly the worst moment? Are you acting without thinking, or are you acting out your resentments? This relationship is a difficult nut to crack, but it's not necessarily DOA. If you truly love each other, act like it. Make a conscious effort to be kinder, more understanding, less demanding. Take care to communicate your needs and feelings gently, rather than raising your voice. Give your lover plenty of freedom and give yourself some 'me' time too. This relationship does not flow as naturally as some, but there is much to gain if you are willing to put in the work.