If a Jew marries a goy, r”l, and has a non-Jewish son who never converted.
He then does teshuva and marries a Jewish lady and has another 2 sons.
My understanding is that the non-Jewish son does not inherit his father according to halocho. Would his oldest Jewish son (his second son, but his first from his marriage with a Jewish lady) have a din of bechor for dinei yerushoh?
Yes he would have a din of a bechor for inheritance. Note: This answer is based on the information given in the question without taking anything else into consideration.