4.5 months is kind of borderline so
I'll link this and ask my main question, what if Henry III and King Alexander of Scotland younger daughter Marjorie married? As the previous thread shows there were a lot of problems with suitable partners and so he married quite late, but he could have married pretty early if this proposal had come about.
She was several years older than him but still in her early-20s, maybe 23 or 24, by the time they would be married for a couple of years and capable of producing children. She didn't marry till 1231 in our time line, so while she produced no children she could have produced a couple at least with him.
Granted, this was a little down the line since she was something like his third daughter, but there were other marriage is being made with Scottish nobility at the time as part of a peace agreement and if things work a little differently maybe Henry could marry the second daughter if not the oldest.
If his oldest sister lives longer they only a few years and King Alexander dies, Henry the third's wife and eventually his son could claim the Scottish throne. Perhaps even his daughter although Henry would probably have to fight for this. Or, just marry her to a Scottish nobleman.
How viable would this be end how would it impact English history? Would there be a willing Act of Union in the 13th century, I presume with the name of Great Britain? While it would be over 400 years beforehand, the name Britain was still quite well known at that time so I think would still be what it would be called.