Some thoughts.
1. Re the children born in Cumberland, it might be interesting to look at their baptismal entries and/or birth certificates to see if there are any clues to the Cumberland connexion.
Children of George WREN and Eleanor baptized at Saint Cuthbert, Carlisle, Cumberland, England:
*Caroline bap 21 Aug 1843
*Marian bap 23 Jan 1845
*Jemima bap 3 Sep 1846
Certificate references:
*Caroline WREN birth Sep qtr 1843, Carlisle, Vol 25, Page 56
" death Sep qtr 1843, Carlisle, 25 32
*Marion WREN birth mar quarter 1845, Carlisle, 25 55
*Jemima WREN birth Sep qtr 1846, Carlisle, 25 50
2. I don't see anything odd about children staying (perhaps only overnight - who knows!) with their grandmother. Incidentally, did you notice that Joseph (assuming the FreeCEN record of his surname is an error) was recorded twice in 1841 - once aged 7 with Grandma, and once aged 6 with his parents.
3. It might be worth downloading the parish register entry for the 1830 marriage of George WREN & Helen CARMICHAEL from ScotlandsPeople just in case there is anything which gives a clue.
4. Unfortunately there does not seem to be in the IGI a record of the birth/baptism of a Helen (or variant) CARMICHAEL or a Helen (or variant) YOUNG, 1813 +/- 10 years, Midlothian, mother Janet/Jane/Jessie (likely variants of Janet).
5. It might be worth searching on SP for the death of Janet YOUNG - but it's a common name! Also for the death of George WREN.
Regards,
JAP