I'm really struggling with DD at the moment. We have had some changes the past year, and I really understand that she may be trying to adapt to them. But I don't know how to deal with her tantrums anymore.
An example- right now I am trying to get ready for us to go for a walk. I told DD this, and said that it was time for her to play with some toys while I get ready and have a hot drink (we've been playing together this morning and she's sat with me while I've done some work on my laptop). I explained I would sit next to her while she plays and she can show me what she's done, but I'll be getting ready so I won't play, just watch. She was fine, chose her duplo, but as soon as we got it set up she starts whinging. I go over everything again, we have a quick hug, I ask her to build me something, the whinging escalates into crying. Ad nauseam, except I say it's enough now and she needs to have some time to play otherwise we won't be able to go out as I won't be ready. She then has a full on, screaming, kicking tantrum, calms down, we have a cuddle, she says she wants to play. She's just sat down and it's started again!
I've ended up just turning the TV on because I'm starting to lose my temper. She said herself the other day "I have time to play with grownups and time to play by myself". And it's other things too, the other day she screamed because she wanted to get out of the bath but refused when I asked her to stand up 
I know toddlers are illogical but it's really getting to me. I've tried cuddles, I've tried being firm, she sometimes goes to her room to calm down (not punishment, she will take herself off there or we take her if she gets very aggressive but we get her a book and pat her, then say we'll give her some time to calm down). I can't hug her because I get kicked and sometimes I feel like that's what she wants, she will just sit on me all day or climb on me and that's not plausible.
I'm just running out of ideas, we are very close and she has a very loving, happy family. The changes are a new pre-school and a new sibling but we've done lots of talking, she's very happy at her new place and she loves her baby brother, and he is now 6mo so she's had plenty of time to adjust. She's not missing out on affection or time with us, we have time on our own with her too. I just need some advice or reassurance? Please be kind.