Nettlecake, I think you're being quite wonderful about this. As beela mentioned, you've stick with the thread and seem eager to accept advice being given. For that I wholeheartedly commend you.
I don't have anything more to add except some things that have already been said:
DD seems overstimulated and seems to have begun to equate time with you as a bit rushed, a bit GO GO GO and that may be perpetuating her behaving in that manner.
I have a 15 yo, a tonne of nieces and nephews and I was a professional nanny so I have years of experience with toddlers and, as disappointing as it may sound, the only way to help DD out of her obstructive behaviour is to help her unlearn it.
Walking around with her means that she has her way. Try working at home first, at dinner time, say, and asking her to remain in her high chair for a few minutes after she's finished. Explain why (mummy and daddy are still eating, dinner isn't over yet, etc.) and don't be afraid that she won't understand the nuances of the behaviour you expect or your reasons for them: She will. Perhaps not down to details but she will understand the gist of what you expect.
And she will rebel! She's used to things a certain way and she won't like the idea that they are changing but be firm. Perhaps set a certain small time limit that you would like her to sit for after dinner. Then, once the time is up, explain to her that you're happy she sat and that she may now get down from the table, but be FIRM when she resists. If you keep the time small to start with and then SLOWLY extend the time once she gets used to it and can sit, she can learn at a healthy pace what it is that you want from her and she can be proud in making you happy when she's done as you've asked. She won't even realise that you're stretching the time sitting because, like it or not, children of that age have no concept of time. I believe, eventually, if she is given no other option but to sit, she will learn to sit. If she's not given the chance to be taken out of the highchair until you decide it's time, she will stop expecting to get out of the chair. When she does finally start sitting for the short amounts of time, as each one is up, praise her, thank her, let her know her behaviour was what you wanted, what you expected of her. Rewarding good behaviour helps to positively reinforce what she's done right and will show her that she doesn't need to misbehave to have mummy's attention.
I think the something similar could be done with throwing. The next time she throws something, grab the item and give it back to her. Look her in the eyes and say clearly "No. Please do not throw things." - If you have to kneel down to get to her level, please do so - eye contact is super important here, she needs to know you're serious. Repeat as necessary. It may be that you have to remove the object thrown and this would be particularly effective if it's something she likes but has thrown in anger. Removing the object and then looking DD in the eye as you say "No. Please do not throw things." as above.
None of this will be easy and it will take time as you have to SHOW her what is expected of her. This will be easier if it's just the two of you, at home, where she can have your one-on-one focus and attention. That will help remove the immediate desire to act out to gain your attention like she would at a cafe.
She won't learn it overnight. But, if you're consistent and firm with her when there are rules and praise and thank her when she does what's expected, I think you'll find she starts to behave quite differently inside and outside the house.
*The above is entirely my opinion and your mileage may vary but I have personally raised three children, raised four professionally and had/have a hand in several more. Please, genuinely, ask if there's anything you'd like me to clarify or expand upon.