I completely understand that your DH didn't mean to hit her. I also understand exactly how difficult it is to deal with meltdowns when the child is being physical.
Lots of us have stories about how we accidentally injured one of our DC. It's a normal part of life - accidents happen. It only becomes problematic if the accident happened due to a lack of regard for safety eg/leaving hot hair straighteners out on the table where a child could touch them,
The very big difference with your situation is that you acknowledge that your DH used "excessive force". That is something very different to a run of the mill accident where a child gets clonked on the head while a parent is doing housework.
It sounds as if your DH lost control. Even though he might never raise a hand to your DD directly, if he can't keep a lid on his temper he will put her at risk.
As some others have said, I don't know how he's managed to leave a hand imprint on her - that really does suggest a lot of force was used and at extremely close proximity to your child if he's accidentally caught her.
I'm glad to see you acknowledge you need help. It may well be that a social services referral is what you need to get access to services. There are parenting courses you can go on, as well as specific courses designed to teach you how to deal with a violent child.
Worth mentioning that I speak as the parent of two autistic DC (and I'm autistic myself), one of my DC has attacked me many, many times over the years, sometimes to the point where I've required medical treatment. I really do know how hard it is so please don't think I'm waving that away. But I also know that you can't lose control of your own temper, no matter how difficult things are. An adult man hitting a child hard enough to leave a handprint is a serious matter. He may not have meant to hit her but you still acknowledge that he used excessive force so that can't happen again.
You need to make sure an EHCP has been applied for, if not, this needs to be a priority. And you need to ask for input from CAMHS/the disability team for help managing your DD's outbursts.
Is she at the right school setting? My DS was infinitely worse when he was stressed at school - when he moved into a specialist setting the violent outbursts reduced (but didn't completely go away).
Do you know what triggered her meltdown? Do you understand what she finds difficult? Meltdowns are a form of communication so getting to the heart of what she's struggling with is key to making life easier for the whole family, but especially your DD.
I'm sorry this has happened - it's really hard for all of you.