Thanks again Gillian.
We spent five days in Ambleside back in early July which gave me chance to get some familiarity with the area - especially driving back and forth to Kendal, passing Staveley, as well as drive up both Kentmere and Longsleddale. But not enough time to visit the archives.
I think part of the trouble in tracking these folks down is that (a) the IGI coverage of the outlying parishes of Kendal is patchy and (b) the transcription of records of the outlying chapels into the Kendal registers is confusing and incomplete.
It looks like the family are likely to have patronised the Staveley chapel/church since there is a small batch of entries in IGI, transcribed from Staveley by an LDS member, which includes the marriages of the children of the older Henry Dowthwaite and his wife Ann Hutchinson, and also a batch of baptisms for the children of Henry and his second wife, Jane, which appear to be extracted from a combination of parish registers and bishops transcripts for Staveley, but only covering about 1813 to 1857.
The chapel at Kentmere is another possibility, and the IGI again has recordsw from about 1813 which include some of the grand-children of Henry and second wife Jane.
Before 1813 I gather that all the chapel entries were annualy transcribed to the main Kendal registers and therefore ought to appear under Kendal. But hnery doesn;t. Therefore seems most likely he might be buried in the pre-1813 Staveley register.
The other children of Henry Dowthwate and Ann Hutchinson Do appear in the Kendal enrties ON IGI. but the younger Hnery does not.