I would also like to suggest a perfectly plausible alternative suggestion.
You mention that your suspicions came about largely because the first child is born when the mother was 15, and that her marriage to the "Handley" husband is three years later. Were she rather older, I would probably agree with your assumption that the father is not the same person as the husband, and certainly there is no proof there of who the father of the first child is.
When we consider the age, however, it is entirely possible that the two young people were a couple all along, but could not marry because either his or her parents would not consent. They certainly could not marry when she was only 15, nor is it likely that his name would be included on a birth register, since that would be tantamount to admitting to what, legally, constitutes statutory rape.
I suggest that a perfectly reasonable alternative is that two young people, carried away in the moment so to speak, had a child by accident, remained together and were married as soon as parental consent was forthcoming (or perhaps when he reached 21?) After all, even three years later she would still only be 18.
I have at least one instance of a couple who were together for about 25 years (until he died) and had at least 11 chidren before getting married 14 years after the birth of the first child.