Do you want to discipline her or improve her performance?
If you want to improve her performance, you need to speak to her face to face, letter or email instead is not really on. I would ring her, say you have some concerns about her performance that you need to discuss with her and arrange a time to meet, without distractions of children or anything else.
Write down everything beforehand, make a note of all your concerns with examples of when she has done each of these things so she is clear what the problem is. Give her a short timescale to make drastic improvements, arrange a follow up meeting to take place after a couple of weeks to review it, make clear that disciplinary action will result in a lack of improvement.
If you want to go straight to disciplining her, you must put your concerns in writing. I would ring her first, let her know that you have concerns and are considering disciplinary action, you will be writing to her to outline these.
Then put it in a letter, outlining concerns, giving examples, inviting her to a meeting with sufficient time to prepare, and making her aware that she has a right to be accompanied by a union rep if she wants to. Ensure she lets you know if she wants to take advantage of this right.
Hold the meeting, hear her case, then decide what level of warning is appropriate. Write confirming this and giving her the right to appeal it, and tell her how she should appeal it and by when (letter to you within a week, for example).
It is possible to skip straight to a final written warning if you feel the concerns are serious enough, or even dismissal if it's really serious gross misconduct. I would say this isn't that situation though. A written warning would be fine, if you do that state in the letter that this is a written warning which will remain active for (say) 6 months, during which time any further concerns will be taken extremely seriously and will automatically result in further disciplinary action.
If you've had no previous discussion with her about your concerns, I'd advise considering the first option rather than leaping straight to a warning tbh. You can as I say make it quite clear that any repeat will result in disciplinary action.