That would suggest that Jane had left a sick child. She doesn't make any mention of discovering that her child is sick, it is Russell that talks about his child being sick and using washing machine etc.
I don't think any mother would leave a sick child. One of the children was not too well, earlier in the day and she was probably keeping a close eye on the child, for this reason. I do believe that they were all on the beach later.
Excerpt:-
Yesterday, the witness did not go for breakfast because she had a tennis lesson scheduled for 9 am. It was her partner who took the children for breakfast, having subsequently taken **** O’Brien to the Kids Club.
Due to **** O’Brien being unwell she did not go to the Kids Club that day and went with her father to look for the witness. They arrived at about 9.30 having waited for about 30 minutes at the tennis courts (8) for the tennis lesson to finish
excerpt:-
After the lesson, the witness went with her partner and daughter **** to the beach (7) where they remained until about 12.20. Then they had been to fetch **** from the Kids Club.
http://themaddiecasefiles.com/post412.html#p412