What is an appropriate way to handle this?

[BiscuitStuffer]

2 year old DD becomes like a dog with a bone with something that someone else is playing with and grabs it and just won't let it go. The other child is often hanging on to it too. There is no reasoning with her and the more you ask her to let go, the harder she hangs on to it.

I am currently just giving her an ultimatum - e.g. let go and return item or be put in the buggy / sit on the floor or some other 'consequence' that I can think of. That works but I can't help thinking that it's a negative way to deal with it as I seem to be dishing out these threats quite often.

What do you do??

I could sometimes get DS1 to share/take turns when he was like that - needed coaching through it, couldn't just say share and leave him to get on with it. Sometimes I could distract him with an alternative toy. If those both failed then like you I would give ultimatum.

As you've already tried asking her to give something back, I would try just taking it from her and giving it to the other child - without comment - and be ready to pick her up (as soon as you've take the toy away) and whisk her off to do something else, hopefully the distraction will be enough to avoid a tantrum. But if it isn't and she keeps trying to get the toy back just be firm and keep physically taking her to different areas until she does calm down.

I wouldn't bother with the talk about sharing, taking turns, being fair etc whilst this is going on as she will obviously not be in the mood to listen and digest. Have the talk about sharing etc when you are playing with her and she is in a good happy mood and is more likely to listen.