First a little bit about how the variants of the royal arms granted to members of the Royal Family work. Children of the monarch use the Royal Arms of the United Kingdom defaced with three labels, Grand Children of the monarch have five labels. The exception is the eldest heir of the heir apparent (Prince of Wales) who uses three labels. In each individual coat of arms the labels bear distinctive insignia, to differentiate the arms. These can be all sorts of symbols, the most common are anchors, roses, thistles, red lions, red crosses (St Georges Cross), seashells and even hearts. Wives of Princes use the arms of their husband impaled with either the arms of their father or the arms they used before marriage (depending on if she was an armiger or not).
|The arms of Prince William and Kate|
My first idea was to place the red seashell of her father in the centre label of the Princess' coat of arms, The flanking labels bear the acorn from her mother's arms.
Another proposal uses all three acorns, alternating with hearts: