Regardless of if the EWO gets involved or not, the situation can't continue for the sake of both her children and all the other children in the class.
Keeping them off and saying they are ill, rather than taking them late is not the answer. That will just lead to further investigations as to why they are consistently ill. Might get a bit more complicated than just a chat with the EWO.
She needs to look for answers and strategies.
Why does she sleep late?
Does going to bed earlier help or make no difference? If the length of time she sleeps makes no difference, then maybe there is a medical problem (melatonin levels??)
The 2 alarm clocks, are they set for the same time? Try 3 (or more if need be) and set them all 5 minutes apart, starting with at least 30 minutes before the latest time she needs to be up.
Prepare clothing, bags, lunches etc etc the night before.
Get the kids their own alarm clock and ask them to jumpon wake up mum too.
How old are the kids? Can they take on a certain amount of responsibility themselves for getting ready for school (I still struggle with mornings so DS1 makes breakfast & both kids get ready before waking me).
Sorry, this is long. Will try to think of more stuff that I used to help me when I was at my lowest and needed plans to make sure the kids were sorted.