I found this article about the possibility that the Buddha has no wife and son:
There are next to no details about his childhood. The Buddha tells us that he was very wealthy, having separate homes for each season, and eating only the best foods (Sutta on Refinement, AN 3.38). The Buddha tells us that despite this refinement he was horrified and humiliated to see the indignities of “aging, sickness, and death” and considered that these would happen to him too. “Should I not seek a release from aging, illness, and death?” he asked himself.
He next tells us that he left home as a young man. There is no mention of his father’s efforts to protect him, or his going out and being shocked by first seeing the “four sights” after a life sheltered from them. He just noticed aging, sickness, and death like anyone else would, but had a more profound response to them than the average.
Not only is there no mention of a wife or child in the Buddha’s recounting of his renunciation, he seems to suggest that he was still living at home with his parents: “So . . . while still young, a black-haired young man endowed with the blessings of youth in the first stage of life—and while my parents, unwilling, were crying with tears streaming down their faces—I shaved off my hair & beard, put on the ochre robe and went forth from the home life into homelessness.” (The Sutta on The Noble Search, MN 26).
The absence of a wife or child is striking. Without the claims of later tradition, we would assume the Buddha had left home as an unmarried youth.
The suttas do explicitly identify one relative, the monk Nanda, as the Buddha’s cousin, son of his maternal uncle (Ud 3.2). The specificity of this identification only makes starker the lack of similar identification when other characters traditionally believed to be the Buddha’s relatives are mentioned. Neither Rahula nor Mahapajapati appear with kinship information. And there is no mention of the Buddha’s former wife.
We get some more additions of a fantastical nature from a later stratum of material in the suttas that are rife with supernatural details. It is in this strata that we learn that the Buddha was a prince whose father was Suddhodana, that after he descended from Tusita heaven to be born to the rejoicing of the gods, a Brahmin made fateful predictions at his birth. Here we learn of his miraculous birth, of lotuses sprouting under his infant footsteps and him pronouncing his identity when only a few minutes old.
It is in the Cullavagga, the stories explaining each rule in the monastic code, that we first hear that Rahula was ordained as a child, and that his mother, simply called “Rahulamata” (Rahula’s mother) sent him off to join the Buddha with the poignant words “go get your inheritance” (this is a cautionary tale of the pain that a child’s ordination can cause parents). This story does seem to suggest that the Buddha was Rahula’s father. It must have been based on a familiar, older tradition, but that tradition may still have come to be hundreds of years after the Buddha died (it was written down between 500 and 1000 years after his death).
The legends of the Buddha’s family are elaborated in various versions by the Buddhacarita, the earliest full biography of the Buddha, written by the poet Asvaghosa in the first century CE; the Lalitavistara, a Mahayana/Sarvastivada biography dating to the third century CE; the Mahavastu from the Mahasamghika Lokottaravada, which was composed incrementally until perhaps the fourth century CE; and the Nidanakatha from the Theravada tradition in Sri Lanka, composed in the fifth century by Buddhaghosa. Most of our ideas of the Buddha legend come from these works.
It seems that EBTs do not see the Buddha was a married man who left his family for enlightenment quest.