Helena, I do indeed think your daughter is a pretty typical 4-year-old. Also I think she is being pushed at school and possibly at home because you so want her to perform in the way her teacher expects her to perform.
You say she can count to 20, but does she really know that 19 is one more than 18? Or that 16 is one less than 17? Saying a series of numbers correctly in sequence does not mean that a child understands what is called one-to-one correspondence. Nor does reciting the alphabet correctly mean that a young child is ready to recognize the symbols either individually or grouped into words.
Do me a favor and give your daughter this little test. Set out a row of 10 small blocks (or beads, plastic spoons or almost anything you have) and ask her to count them for you, putting a finger on each object as she counts. Chances are she will do maybe one, two and three correctly and then touch number four two or three times before going on with the series of verbal numbers. By the time she gets to the 10th object she may have made contact with the objects 15 or 16 times. In other words, she doesn’t yet realize that each number word she says stands for a specific quantity.
In relation to letters and words, make sure you read a book to her every day. Point to an occasional letter (don’t try whole words yet) or number and ask her what it is. If she doesn’t get it right, tell her in a matter of fact tone and continue reading. Don’t spoil the joy of the reading with constant quizzes.
As far as her distractibility and crying at school, I would request an appointment with her teacher to talk about this. Try not to be accusatory and say things like, “Well, she’s not like that at home.” Assume that the teacher is as interested in helping your daughter as you are. Ask her for suggestions of things you can do at home to help. Finally, can her 10-year-old sister be part of the solution? She might be able to provide a more stress-free “number teaching session” than you can.
Our parenting advice is given as suggestions only. We recommend you also consult your healthcare provider, and urge you to contact them immediately if your question is urgent or about a medical condition.