Both Adam and Arthurs' births calculated from their ages given at death (never that reliable!) are about 1823. So if Adam was born say late 1822/early 1823, Arthur could have been born early in 1824 up to when his mother died in the April.
The children were all baptised together later in 1826 in St Botolphs in Aspley Guise. William Hutton, their Uncle, and his family, seem to be the only one of Michael Hutton (the children's grandfather)'s family attending that church - I noticed that as I worked through the films of the church books. William Hutton became the Church Clerk if I remember correctly. I suspect the most of Williams siblings attended St Mary's, Wavendon.
..........I can't wait to look at the Wavendon film.
Joseph Hutton, his second wife Sarah, his son John and Grandson Henry James Cooper are all recorded in the St Botolphs church books.