It sounds like your dd is going through a new stage of independence.

Can you really look at your expectations and see if they need adjusting? It is easier to cope sometimes if we know there is a reason, so perhaps you could see this as a stage that needs to be managed/survived rather than a problem needing a solution itms?

With the playground example, I think it is important not to threaten things you can't follow through with. You won't leave without her, so I would be hesitant to threaten that.
After asking her to leave, perhaps your Dh could have just calmly said 'I'm going to wait in the car so come when you're ready' and see what happens. That would only work if the car was in sight of the park, otherwise I would emphasize how cold and dark it's getting and then 'sell' them something fun to do at home (let's go home and make milkshakes what's your favourite flavour?)

I don't have a 6 year old, but I think all children test the boundaries as they grow. Our job is to help them find the new boundary suitable to their age, but in a supportive way.

It's late so sorry if this vague.