Hi Judy...
In doing a quick scan of the 1870 census that you mentioned in your post.
1870____ Father Jeremiah is 40 years old b. abt.1830
I took this info and forwarded to 1880 census.
It appears that the family has had a bad turn of events..
Father Jeremiah__ b. abt 1829 is living in a boarding house on Thompson St. NYC
I looked to see if this was some type of Institution but there isn't any mention on the census sheet.
Jeremiah states that he has been unemployed for five months out of the 1880 census year.
Although, he says that he is married, I'm unable to locate Catherine--- so far.
It isn't unusual for men to say they are married even though they no longer live with the spouse. The woman may state that she is a widow_ only later one finds that her husband is alive and well.
I've found various individuals named in the 1870, that are living with other families.
There is no way of putting them together in this family group without more evidence of same.
If you have access to census images, you may want to try and trace this family through 1900 census.
Sending Warmest Wishes for the Holiday Season,
jelora