Hi Tobysmum - I got excused from jury service as my DD was only a few months old at the time and I was still breastfeeding her and I also said I couldn't possibly arrange short-notice short-term childcare for an unspecified period of time.
Good luck with your letter. IME there are some reasonable people out there. It probably works out for the best anyway as if you were to go and not concentrate on what was going on for worrying about your child at home that wouldn't help anyone.