Unless she is showing this behaviour at school too when she will be receiving instructions from the teacher, then I do not feel it's ODD or PDA.
You may feel this, but it's not true, especially in the case of PDA at this age. Children with PDA can be master maskers.
As for the poster with the autistic child displaying ODD, it's more likely to be PDA if autism is also present as PDA is a subset of autism.
From what you're saying OP however your child doesn't display any autistic traits? Is that right? They can look v different in girls.
Does she struggle to sit still?
It could be ODD, that often comes with aggression and violence though, but would tally with the lying whereas autistic children are generally crap at lying. It could also be developmental trauma or attachment issues as you ponder on in your OP.
My first thought is that it sounds like you're possibly making a lot of demands on her, if by 11.30am you're in tears with her refusals.
So my first step would be to reduce demands. Massively pick your battles. Really think about WHY things are important to you. Does it REALLY matter if she gets up from the table? Why? Choose maybe 2/3 things that are really important to you to enforce (they need to be specific so you can't choose, say, "doing as I say") and forget the rest.
Secondly it sounds like she could be dysregulated going between both houses and struggling with having two parents telling her what to do, possibly different rules in each house, and not feeling safe?
Have you done much work on this? Does she open up and express her emotions?
How much fun and laughter do you have on the average day?