OP this sounds really tough! It also sounds pretty normal to me. Especially given there’s been so much going on for her in the past year - potty training, a new baby (massive!) starting nursery, possibly dropping her nap, possibly sleeping in a big girl bed? And those are just the ‘obvious’ changes, none of the massive developmental stuff that’s been going on for her.
The key thing is, if she is crying and tantruming for your attention, she’s likely to be getting a response from you and her dad that is a bit irritable at times (you’re human, and that’s normal), but it won’t be meeting her need for that extra nurture and comfort that she is showing you she wants. She doesn’t know how to put that into words, because she’s three, so she just keeps screaming, even though the screaming doesn’t quite lead to the reassurance she craves. And because she’s not quite satisfied, the cycle just self perpetuates.
If I were you, I’d lean into it as much as possible for a few weeks, and then reassess. That doesn’t mean doing everything, but doing as much as you can with her without her having to tantrum to get you, so you start to break the connection between ‘tantrum’ and ‘getting mummy’. She gets mummy lots without needing to tantrum. And then make sure you prepare her if you’re ‘leaving’ her as much as you can, and try to be specific about how long until you’re back.
Are you able to ever go out just the two of you? Completely shower her with your attention and love when you take her to the park for an hour, just you two. I would also suggest building her relationship with her dad, so think of something she would love to do (ideally a weekly activity) and he takes her every week. It’s her special time with daddy. He is totally involved and connected with her, no phone and no distractions.
It also might be worth looking into books you could read with her about the impact of a new baby or about being apart and coming back together, whatever your sense is of the root of the issue for her. The invisible string is a good place to start (often recommended for children who are adopted, who struggle with the idea of adults leaving and coming back) but there are probably more tailored choices for your specific situation. That could help give her some language around what she is feeling.
That’s another point, actually. Try to label her feelings as much as you can, so that she starts to learn the language she needs to tell you what she needs, rather than screaming. “It looks like you’re feeling really worried and sad that mummy has to leave now. I’m so sorry you’re feeling that way. I am coming back at [specific point relevant to her, eg, after tea]” “It looks like it’s making you so cross that mummy has to care for the baby right now, it can be so hard to share mummy. Sometimes I am busy with the baby, but I love you all the time, darling”. “I wonder if you’re feeling angry that mummy is looking after the baby again, and isn’t with you?”
I promise this labelling works. My DD is a similar age and has a baby sibling too. She often wants me preferentially and will go through phases of being a bit screamy about it. At the moment she is doing a lot of “help, I’ve fallen down!” “Help, I’m falling!” when she wants my attention. I consistently tell her that it’s okay to just want her mummy, and she doesn't have to pretend to fall down. She can just ask me for a cuddle, or for some attention and then I give her a big cuddle. She has taken this on and started to ask for a cuddle or say she needs some attention instead. It’s positive because she is developing awareness of her own internal world and learning that it’s okay to be upfront about her emotional needs and she can expect to have these met in her key relationships. She even told me she was “frustrated” twice this week, instead of screaming. I was delighted! I’ve been working on frustrated for a long time!
anyway, I’m going to stop rambling now. I’m wide awake because the baby hasn’t woken up like normal for a feed ha