I think your Isabella Hoggarth is the one who appears in the IGI as the daughter of Joseph and Agnes, b. August 1st 1819, christened at Windermere.
Unfortunately I don't have the baptism records for 1819, but I do have baptism records for other children of Joseph and Agnes. The dates may contain errors because my copy is hard to read, and they seem confusing:
1816 John, son of Joseph and Agnes, Lindeth, farmer.
1817 John son of Joseph and Agnes, Lindeth, farmer, b. Feb 11th, christened November 2nd.
1826 Joseph son of Joseph and Agnes, Lindeth, farmer.
Lindeth is still there. It was a large estate containing several farms bought by John Bolton, a Liverpool merchant who made his fortune in the slave trade and lived at Storrs which is now a hotel. Joseph Hoggarth appears as his tenant in the 1829 land tax for Undermillbeck.
Surnames can be very local, and Hoggarth isn't really an Undermillbeck name - the Hoggarth family originally came from neighbouring Troutbeck I believe, and the painter William Hogarth was related to them. As a tenant farmer, Joseph is likely to have moved to Undermillbeck from somewhere nearby. However, there one or two Hoggarths appear in the 1777 window tax.
I don't have records for Staveley, but there were certainly Studholmes in Staveley - Wiiliam and Ann stick in my mind. If I come across anything, I'll let you know.