It's hard to tell online how much someone already knows, so if this is off the mark, I apologize.
Catholic parish records list the mother by her maiden name, so the Isabella's birth on 16 Nov 1857 in Ballynahinch isn't illegitimate. If it were, there would be a note in the register, I am pretty sure.
So you would be looking for an Isabella Hedifin's marriage or death to see what happened to her.
Can you put your Samuel Hedifin in the Ballynahinch area in 1857?* If so, it might be an earlier marriage for him. Again if so, can you find a burial record of Rose Hedifin between 1857 and 1863? (Civil Reg.of deaths started in c. 1864, so you would have to hope for a burial record).
*edit: What was his occupation when he married in Newtonards in 1863? If farmer, he probably didn't move around a lot. If constable, teacher, etc., then he'd be more likely to be the same person who married Rose Gilmer. What was his father's name? Where was his father? Griffiths was about that year, were either James or his father in Newtonards or Ballynahinch - but again beware of 2 people with the same name.
If you can't put him in that area in that year, then there could have been two different Samuel Hedifins.
And you would need to investigate the Rose Gilmer who married James Savage in the 1860's. (I couldn't find the record in a quick look). Was it also in Ballynahinch? Were there two Rose Gilmers? Can you find Rose (Gilmer) and James Savage on later records, e.g., births of children, 1901 Census?