My DD (8) always embarrasses me

You can work with your DD to change things hopefully.

But your DH is another thing, he sounds nasty and it looks like your DD is picking up behaviour from him. He needs to go.

The only thing that stood out to me was your husbands comment. You said you children didn’t hear but I promise you they do and they will see that as an acceptable way to talk to you in public. That’s not normal in any relationship

It’s obvious where your dd learned her disrespectful behaviour op. I’m sorry but the minute anyone called me a “wierd little bitch” they’d be out of the house, or I would, with my dc with me!

You are never going to feel better with him if he speaks to you like that. Your children will be picking up this awful behaviour from him, please protect yourself and them from this abuse.

How are you ever going to feel better in an abusive relationship??

You will never feel bbetterwhile still in this situation.
And your children, however bratty, deserve to have their wellbeing put first.

Your daughter is a red herring. The real issue lies elsewhere and you're unlikely to feel better whilst you remain tethered to him.

Your husband had zero respect for you and sees you as someone lesser and wrong. Your DD is treating you in the way she's learned to. If I were you I'd take your DD and get yourselves away from his toxic influence so you can teach DD that you are a person worthy of respect, because this will get worse not better, from both of them.

This is exactly what's happening.
And @Struggle1 you have been so badly weakened by the way your H treats you, you can't defend yourself against an 8 year old. Instead, you sat there going red and getting upset.
You should have told her sternly "you do not say your mummy is lying, that's not OK. And you're wrong DD, what I said was true".

Would have, not could have …

This. Anything less and you’ll be in for years of trouble. Mine could have been in massive trouble if they did that.

I agree that you need to work on your confidence. I'd go nuts if any of my kids spoke to me like that.

There's nothing wrong with correcting your daughter in front of the other parents in that scenario and follow up with "please don't interrupt when I'm talking" and then return to your conversation.

I think there's probably a lot more going on here though. Your husband's response is very, very unpleasant.

Also, you say "always"
Does this happen often?

I would giver her a bollocking
How dare she.

Also you need to divorce him.
No questions asked. I don't need more info.
To not divorce him means you have to suck up your daughter behaviour because why should she respect you?

@Struggle1 ahhh please don't give it another thought! She sounds like my 8 year old DD, and in the moment it's very annoying!
You've spoken to her, if such an instance happens again, remind her not to interrupt.

The only thing that would annoy me to the point of still thinking about it, would be the comment your DH made.

Why are you more concerned by what an 8 year old has said to you than a terribly abusive comment from your dh?

I'm guessing your lack of confidence, anxiety, and overthinking is at least partly due to your abusive partner?

It is never acceptable to call someone a "weird little bitch". He's disgusting.

I'd advise you to have therapy to overcome your issues and get stronger. Once you feel stronger emotionally, you can consider your options regarding your piece of shit partner.

You can usually self refer to the NHS Talking Therapies service. If not, your GP can refer you. Or you could access therapy through a charity like Mind or a smaller local one.

That’s kids for you, happened to me loads of times! I agree it’s absolutely annoying! I would correct her in future and say firmly ‘no you are wrong’ and change the subject and distract her - look at how nice ‘ what other kid you see In the distance’ is doing lol that way you avoid a confrontation.

I'd have been told firmly to be quiet and remember my manners if I'd ever done that. Children need to be taught how to behave - but it's not always easy.

Well exactly.

Maybe you do need to work on your self confidence as @ButWhatAboutTheBees suggests. But it can't be doing it much good when your DH is so dismissive and unsupportive.

I suggest you focus on him as the problem not your DD

You say your mental health is bad OP - I get it as mine can be too. But this stood out to me:
I tried to talk to DH when I got home as I was feeling upset but his response was he doesn’t care and doesn’t have time and has to take his dad somewhere. He called me a weird little bitch (kids were in car and didn’t hear).

I wonder how much your 'D'H's responses affect your mental health, far more than your DD's actions.

He called you what now??

Children copy their parents, and it sounds as if your husband has modelled having zero respect for you which your daughter is copying.