Martha (Nichols) Heath - Death? Divorce?

I'm wondering what the story is with William Heath and Martha Nichols. They married in 1829, and according to the Amherst vital records had Jane (whom I believe to be Cynthia Jane, named after Martha's mother) in 1831, William c. 1833, and Daniel in 1833. However, the records of Jane and William only give William as the father. Then William (father) was declared a pauper in 1835, and Jane and William were under the care of the town of Amherst. Daniel was living in the household of Alfred Baker in 1840. In the 1850 Northampton census, Cynthia Heath, age 19, was living with the Stoddard family, the father Solomon having died.

Amherst Vital records:

HEATH

372 - Jane, d. William, ca 1831, at Amh., under care of Town of Amh. 1835. [JAS] [I believe this to be Cynthia Jane.]

372 - William, s. William, ca 1833, at Amh., under care of Town of Amh. 1835. [JAS]

372 - Daniel E., s. William & Martha (Nichols), ___ __, 1833, in Palmer, schoolboy and farm
laborer in Amh. 1840, lived in household of Alfred Baker. [JAS]

610 - Daniel E., ___ __, 1833. [GR2]

372 - William, s. Daniel & Polly (Lewis) (2nd w.), ca 1807, at Amh., bpt. October 11, 1807,
pauper at Amh. 1835, aided by Perley Wood, of Monson, the husband of his sister, Polly
Thayer. [JAS]

Though both William (son) and Daniel were born ca 1833, I assume the first son would be named after his father. Therefore, I would guess William was born first, maybe in 1832. If they were twins, it seems strange that their records appear differently and that only one of them was under the care of the town of Amherst.

William (father) married Ruth Pease in 1837 and they had 5 children.

So what happened to cause William to be declared a pauper and 2 of his children to be under the care of the town?
This record for a death in the Amherst records is probably Martha:
HEATH
372 - _______ (Unknown) w. William, perhaps late in 1835. [JAS]

But it says "perhaps", so I don't know how "official" this is.

Does anyone have more info on this family?