PS homemaker I am sure posting your situation here can make one feel vulnerable, you do want to defend your opinion and can naturally feel posters who agree are your allies and any who don't agree are being very negative or don't have the full picture. We don't, but none of us do. Maybe not even you.
Please do take a breath and have a think, your dh is definitely in the wrong but what is the best way to get things how you want?
Make sure he has one or two complete sets of uniform, at his home, and ideally, these are his responsibility to clean. She arrives at his house in her uniform and he will have her clean next set of uniform there. He is then responsible to clean the set she was wearing when she arrived at his house and then to it ready at his house for next time.
If him if he can do this. I bet he can.
He then drops her at school early, not just on time, to allow for any kerfuffles last minute, and then takes your son round to you.
Presumably, he must be able to do his own laundry, including shirts etc so a child's school uniform is a doddle.
If not, he can find a service that can do it.
Or if you really want to assist him you could send her with a clean uniform for the next day, that is your choice. If he does not have them mid week you would be doing all the uniforms so really it is not more work for you to provide a clean uniform. And you will still get your night off/out.
I think he should be able to clean one uniform once or twice a week, but I feel this issue is more about the uniform than the lateness.
PLEASE do not see those of us who have a different opinion as the enemy, we are trying to help, not judge, really. I think your dd will cope with this all if you can show her a way to manage her emotions. It is horrible when our kids are upset.
You are a good mum. Try and find a way through.