she'll keep it up for as long as required.
Does this mean that someone always gives in to her before she gives up the behaviour?
It could be that she ought to be assessed by a paediatrician because, as Pag said, it is easy to assume it is our parenting that is causing the issue when, in fact, it is the child's neurology.
However, you need to think very carefully about whether she has learned that she can basically control you by screaming loud enough for long enough to get what she wants.
Toddlers who try to control adults, don't really want to control adults; they want to find out how much they can control adults. They need to find out that they basically can't and be enabled to learn where having their say ends and unreasonable behaviour begins. Have you given your DD very clear boundaries to help her work out exactly where she stands or do those boundaries change?
If it could be that she has learned that she can decide who does what with her and impose her will by screaming/crying/tantruming, she will feel unhappy and insecure.
I would try making some pretty clear rules and sticking to them rigidly for a while.
If she refuses to play with you both together, the game ends and she doesn't get to play with either of you.
If you walk into the room while she's with your DH and she kicks off, he moves away from her and refuses to engage with her until she has accepted your presence.
If one adult starts doing something with her, that adult finishes it no matter what she does in response.
Don't punish her. She is too young and it will just confuse her. Do everything calmly and positively and respond positively very quickly if she adapts her behaviour in response.
If a few of weeks of very clear and very consistent boundaries don't work, I would definitely see the GP and ask for a referral to a paediatrician.