I'm not sure if it's alright to leave out the word "princes", but this is what I would do (unless the sentence continues, specifying the names of the princes: "and TRH, Princes so-and-so and so-and-so).

"In the British monarchy the style of HRH is associated with the rank of prince or princess" (Wikipedia), so I think the English reader will understand that "Their Royal Highnesses" refers to princes.

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Note added at 28 mins (2008-08-10 10:55:20 GMT)
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Note: I would say "His Majesty and Their Royal Highnesses". I think that would make it clear that it refers to the king and the princes.

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Note added at 31 mins (2008-08-10 10:58:54 GMT)
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This is about the British royal family, but it's a similar case (about the queen making a visit with the Prince of Wales and his missus):

As they toured the monument, Her Majesty and Their Royal Highnesses paused by the name of Earl Mountbatten, the uncle of The Duke of ...
www.royal.gov.uk/output/page6083.asp