I'm sorry it's a rough day. Take deep breaths and get a cup of coffee!
First of all, I think it's okay that he doesn't want to "work on it" or try to improve right now. Really. However, it's also okay for you to say that you don't want to write something at the moment. You have the right to that space.
*Alphabet tiles and magnets can allow him to "write" without really having to write.
*He can cut letters out of magazine pages
*You can arrange a time that you will be available to write for him
*He can type in WORD or something on the computer.
And even though I am sure you are already doing this, make sure he knows that you're there to help him work on anything when he is ready to do that. "I know that writing has been frustrating for you. When you feel ready to try more I will be here if you need me to show you anything."
Him not wanting to write is so so common, particularly in boys his age. My Ds was the very same way. He's 16 now and can write fine, but he prefers to type whenever possible.
Time will pass and Dom may end up having gorgeous flowing penmanship and love to write. He may have decent handwriting and just write as needed. He may have not so great handwriting, but he can convey his thoughts okay and prefer to type. These things work out in the end! He's so little yet and he has so much time to explore and develop this skill.