The Cain-Able story is usually assigned to what is known as the "J" source. There's a great deal of argument about when J was writing, but it's usually in the neighborhood of 8th - 6th century BCE. So from a century before the Babylonian exile, to shortly after. It likely however predates J as an oral tradition.

The oldest version of the Romulus-Remus myth we've heard about was by Quintus Fabius Pictor, who wrote in the 3rd century BCE. Unfortunately his work is lost, but was quoted by later authors. He likely was himself quoting oral traditions. So we don't know precisely when the Romulus story was formulated. In any case it likely came after the Cain myth.

In both cases the stories were well separated geographically and created by small somewhat isolated communities. It's unlikely that either story was influenced by the other.

Family killing family was a very common motif in ancient mythologies. In fact reading the histories it was a pretty common motif in ancient cultures' actual histories. Common enough that we have a dedicated word, fratricide, to describe sibling murder. It's likely that both stories were inspired by all too common real world examples.

As mentioned, the Cain and Abel story is likely older. The traditional date used throughout Roman history for the founding of Rome was 753 BC. The Romulus and Remus story does not appear in written form until around the third century BC, although certainly could be older, although it seems safe to say that it then cannot be any older than 753 BC.

The exact date at which the stories in the book of Genesis were written down is a matter of conjecture, but some modern scholarship suggests it was a response to the Babylonian invasion in 583 BC. Certainly by that point the stories would have been much older however.

So it is fairly unlikely that the story of Romulus and Remus influenced the story of Cain and Abel. However, could the reverse be true? The Romans certainly were not shy about adopting foreign influences into their cultural mythos. Certainly they had no problem absorbing the story of the Greek Aeneas from Homer's writing. The Greeks however were one of the major cultural powers of the ancient Mediterranean world. By the time that the Romans were rising, the fortunes of the Jewish kingdom had long since faded. The former kingdoms of Israel and Judah had been conquered by the Babylonians, the Persians, and later the Macedonians by the time the Romans became a major player on the world stage. It seems fairly unlikely that they would have absorbed a story from a distinctly minority and at the time un-influential religion for part of their foundation mythos.