which president had a son names Bennie that died young, didn't swear on the bible at inauguration, is ranked among the least effective presidents ever and ran over a woman with his horse?

Answer 1

The answer and a brief biography are here:
http://www.doctorzebra.com/Prez/g14.htm

Answer 2

This probably the president you want.

http://en.wikipedia.org/wiki/Franklin_Pierce#Presidency_1853-1857

Note that he "affirmed" but did not "swear" his oath on a Bible.

Answer 3

I was not aware of the refusal to take the Oath of Office on a Bible.