Don Trump Jr. Feels Bettina Anderson 'Would Impress' Dad After Allegedly Griping About Kim Guilfoyle's Style (Exclusive)

Sources close to Donald Trump Jr. and the Trump family are sharing exclusive insight into the former first son's rumored relationship with Palm Beach socialite Bettina Anderson.

The eldest son of President-elect Donald Trump was recently seen holding hands in public with Anderson, 38, without first addressing his engagement to longtime fiancée Kimberly Guilfoyle, 55.

A source told PEOPLE shortly after their outing that Don Jr., 46, has been seeing Anderson for "about 6 months" and "even took her on a trip to Alaska and introduced her around as his girlfriend when he was still very much with Kim."

Now, a separate source close to the Trumps suggests that Don Jr. sees Anderson as someone who better fits in with the family — his own Melania Trump equivalent. Melania, 54, notably met Donald, 78, amid his second divorce while he was on a date with another woman.

“Don Jr. has always wanted to look good in his father’s eyes," the source tells PEOPLE. "Someone like Bettina, who is and has been a model, and is in Waspy circles of Palm Beach is something that would impress him.”

A political source also brought up relationship optics, telling PEOPLE that Don Jr. has complained for a long time about Guilfoyle's style, which some people in her orbit have also allegedly criticized.

“Don Jr. has been telling people for months that Kim is so uptight and always dresses so professionally in these kinds of dresses and high heels, and never looks relaxed or casual," the source says. "The tight dresses need to go and she has been told that."

The political source also told PEOPLE that Anderson has wanted Guilfoyle — who was nominated as the U.S. ambassador to Greece by her would-be father-in-law on Tuesday, Dec. 10 — "out of the area" since growing close to Don Jr.

"They are trying to send Kim abroad," the source said, as PEOPLE previously reported. "They waited for the election to pass but they didn’t want the split to get in the way of anything to hurt Donald in the election."

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PEOPLE has attempted to reach Don Jr., Guilfoyle and Anderson for comment on the relationship rumors.