Maybe the children (or the youngest 3 at least (hence the different place of birth from Ivy) were adopted by Jane and taken on by Lois after the former's death in 1898. The children take on the name Newick, naturally, and Lois doesn't actually marry William - hence no birth records or marriage record and William is described as a widower in 1901. Lois takes on the position as a sort of surragate mother (of course it is possible that Lois was married to a Mr Milne and still married, though separated, so marrying William was not on the cards)
The 2 children you mentioned may well have been theirs, and it is quite possible that the pain of losing them so young was too much for Jane, so she accepted providence until........
I have never seen William Christmas, but the other 2 boys were similar in looks (tall) whilst Ivy was small
However I still don't know who Milne was or Lois's official status but I am still convinced that they cannot possibly be her birth children - not while Jane is still living (assuming she died in 1898)
Till tomorrow
Simon