I could have written most of that about my DS who is also in Year 1.
School first flagged writing as "behind" at Christmas and placed him in a catch-up group. Because of class projects being shared during lockdown I have seen his classmates' writing and he is def "bottom of the class". It is illegible without 1-2-1 help sitting over him. I have realised during lockdown that he struggles with everything - forming the letters, size awareness, alignment, orientation, spacing. The pre-cursive letter shapes with the ready to start up stroke and the tail things seem to have sent his brain into meltdown, it's as though there are too many lines and direction changes to compute. Spelling is not even on the radar, he can't write all the letters let alone worry about whether they're the correct letters for standard spelling.
He is a master of ignoring, procrastinating and displacement activity when asked to write. I feel your pain. We find it hard to know where to strike the balance between seeing he really needs to practice, but knowing that pressure is counterproductive.
I think writing for a purpose and stealth learning is the way to go. Could you get her to start a correspondence with some fairies in the garden (you write the replies) or similar? Get her to help you write shopping or reminder lists?
DS is often happier writing on a whiteboard than on paper. Less scared of mistakes and perhaps less tiring too. We have a big whiteboard easel and also A4 whiteboards like they use in school. You can get them with the letters on one side to trace from the Dyslexia shop.
For context, DS doesn't seem to particularly struggle with motor skills. His pencil grip is fine and he has been good with Lego for years. His ball skills, throwing and catching are pretty poor but may be lack of interest or practice as much as anything. He had no trouble learning to ride a balance bike or pedal. There is strong family history of dyslexia and I do wonder about that... but his reading is at age appropriate level (turquoise book band) so the school aren't concerned. His vocabulary is good and he can express himself well, and do mental maths fine, it's just the writing.