Drama is unfolding in David Beckham's family, with 2 of his sons beefing over a woman -- not in a jealous way, but more a question of her motives.

Sources connected to the family tell TMZ … Brooklyn and Romeo Beckham are not on speaking terms because Romeo is dating Kim Turnbull.

We're told Kim had a romantic connection with Brooklyn several years ago, but that's all water under the bridge.

Of course, Brooklyn is happily married to Nicola Peltz now, and our sources say the issue at hand is the couple questions whether Kim has the right intentions in dating Romeo.

Our sources say the feud is why Brooklyn and Nicola were noticeably absent from a recent celebration for David's 50th birthday. Romeo was there with Kim, and we're told Brooklyn and Nicola will not be present at any public family events that Kim is at.

What's interesting is Romeo posted a family photo from Dad's party Wednesday with the caption, "Family is everything" ... and he did not tag his bro and Nicola.

Brooklyn and Nicola also skipped Victoria Beckham's fashion show last month ... and we're told that was also due to the fact that Kim was present.

Our sources say things between Brooklyn and Romeo started to go south in December and their beef has only been getting worse.

Kim's got Romeo's parents on her side though ... our sources say David and Victoria trust her around their son.

Not so much Brooklyn ... who, we're told, feels protective of his younger brother. There's no ill will toward Romeo himself, Brooklyn just doesn't approve of Kim dating him.

We've reached out to reps for David, Brooklyn and Kim, but no word back.

Brooklyn and Nicola live in L.A., while 22-year-old Romeo still lives in London with David and Victoria ... so, it was interesting this week when Romeo and Kim went to a soccer game in L.A. with his famous parents.