I'm sorry you are going through all of this. I know how upsetting these "conversations" are especially when an otherwise nice day gets "ruined" over something as silly as a shower. Except, this isn't a about a shower. It's really about this dynamic:
I had such romantic plans this weekend. But it all went down the toilet because I asked my DBPDGF if she was going to shower before dropping my son off with his Grandma. She got mad because I wanted to take one before going. Then she said fine we will (I must note that she gets mad if we don't shower together). I said no, I don't want to upset you. Just tell me what you want for breakfast and I will pick it up on my way back from dropping my son off. She wouldn't have any of it. She kept on in the shower about why I was wanting a shower. I told her I was sorry multiple times.
As with any dynamic, it takes two. I've highlighted your respective roles. You can't change her side of this dynamic - that's for her to work on. But, you can change your side of this. By the way, this dynamic is very familiar to all of us here and is a very common starting point for members.
The good news is that it can be changed. We focus on ourselves here, and not so much our partners, who we assume aren't going to change and will be difficult. But, we can adjust our expectations for our partners and work on our communication and reactions. For example, most of us would no longer offer any apology based on these facts. No one did anything wrong. You and her juste had different needs and priorities. No one was right or wrong. Same with the deflection about breakfast. It's often better to let her sort out her feelings on her own, than for you to try to distract with things like breakfast or apologies (it doesn't work anyway).
As you change your side of this dynamic, she will react . . . negatively, at first. But, if you stay strong and work on your end of this, things really do get better for you. Have you read our Lessons?