Naming convention with 2nd marriage of woman

Hello!  My husband's great grandmother Mary Hannigan married (don't have name-- will say given name is X) and had 2 children John and Michael.  Michael fits mother's father.  According to naming convention, the first born was named after the father's father, so we know X's father was named X.  X died (assumed) and Mary married my husband's great grandfather Timothy Early/Hawley ( I do not know the names of his parents or siblings if he had any).  They went on to have 4 boys.  Their first son (Timothy's first, but Mary's third) Daniel was born in 1866 and died probably 3 years later. Question #1: Can I assume that Daniel is the name of Timothy's father, even though the "father's father" had already been used with Mary's first marriage? Timothy and Mary had another son, William James in 1868.  Question #2:  Since the name of the mother's father was already used (with Mary's 2nd son from her first marriage), can I assume that William is Timothy's eldest brother? The third son, Daniel was born in 1869, so we know the first child of Timothy and Mary had died and they reused the name.  Their 4th son (but third living), named Timothy was born in 1871.  This appears to follow the naming convention.  Thank you for your advice!