Try developing a scale of problems - big problem or small problem.
Big problems are issues like feeling very sick, falling and cutting herself, being splashed by a passing car and drenched on the way to school, breaking or losing a favourite toy. They are problems that a grownup can help with, and she can and should ask for help without bawling about them nonstop.
Small problems are problems that arise from our feelings. Our feelings are all ok, but they don't need to be expressed by crying, whining, or tantrums. We can use words, and we can trust our adult to listen when we talk about them.
Maybe practice identifying the problems when she seems to be getting upset at home, then decide whether the problem is a big problem or a small one.
Feeling a little more aware of what's happening can take the urgency out of a situation for a child who goes into emotional overdrive.
It might also be productive to ask her how she is feeling about activities she's engaged in - interrupt her when reading, running in the garden, bouncing on the trampoline, watching TV, doing a puzzle, etc, and ask her how she's feeling. When it's coming up to time to get hands washed before dinner, ask her how she feels about stopping what she's doing and moving on to hand washing/ sitting at the table. It can help to keep on practicing identifying feeling.
Before a party, ask how she's feeling when you're getting ready, ask her how she thinks the party will go, what she's looking forward to, what she doesn't like about parties. Take her aside briefly at the party and ask her how she's feeling. About twenty minutes before it's time to leave, ask her how she's feeling, and how she feels about the prospect of leaving. If she starts carrying on, assure her you realise the idea may be upsetting, that you are there to listen when she is ready to talk using her words, and you hope she'll be ready to talk soon.
Remind her that she can talk to you in the car too, and you'll be ready to listen.
Social stories, where a child has a personalised booklet made with photos and text describing any transition she finds difficult, can also help. Basically, the first photo is captioned with biographical details of the child and family, the next page includes details of school, teacher, and friends, next page shows activities and social events. The next page describes feelings she has at parties or gran's or the beach, etc - any place she doesn't want to leave - and how she can deal with those feelings. Can she talk to mum and get a hug? Hold a tactile / fidget/ calming object? Put on headphones and listen to music she likes?