Firstly congrats on the new job, I’ve been out of work for a year and only had a handful of interviews!
May I ask, when you were out of work, I presume you were spending a lot of time with your daughter? It sounds as though she got used to you being around and suddenly you’re out at work, long hours etc etc, and she’s finding the change from “Daddy being there” to “Daddy not being there” difficult. I’m afraid all you can do is be patient with her, as for the tantrums, well, at 2 1/2 she is trying to push and find her boundaries.
With regards to her behaviour when others are around, again if she’s been used to it being just you and her for 10 weeks or so (a long time to a 2 1/2 year old) then she doesn’t want to share – its one of the rules of a toddler, think of her reaction when you play with her fave teddy, its a similar thing.
As Dominic has said, if you react to her tantrums, she’ll push back, then you do and soon it all explodes. I found one of 2 things worked for me and my late wife – ignore the tantrums, if they don’t get a reaction then they’ll eventually work out its not worth it as they aren’t getting what they want. When she shuts the door on you, push it once then leave it, don’t keep trying.
Hope this helps, let us know how it goes!