Recently, it was discovered that Flynn and Rapunzel were inserted as surprise cameos in Frozen, sometime when Anna was singing "For the First Time in Forever". The physical similarities are obvious.
Apparently the couple were just one of Arendelle's guests to Elsa's coronation as a form of respect or tradition with allies. Interestingly, a post from reddit gave a quite reasonable theory:
When a long lost princess is found and becomes married, that would be cause for other royals to come to the wedding.
In Frozen, the King and Queen were leaving for Rapunzel's wedding. But wait there's more! The reason why Flynn and Rapunzel are at Elsa's coronation is because they knew why Anna and Elsa's parents were dead. They felt guilty because it was indirectly their fault the princesses of Arendelle were orphans.
Now, let us go deeper. Is there another reason apart from this why the Queen and King of Arendelle's journey is still so important? Why, family of course! Another popular theory going around was that due to Arendelle's late Queen's brunette hair, she looks very much like Corona's Queen that they could very well be...sisters!
Which could make the lead female characters from the two movies cousins! Now we could finally daydream why the three princesses have similar features.
I saw another "evidence" that the two films are part of the same universe. This time we set our sights at Prince Hans Westergaurd, the surprise villain. He is the youngest in the royal family of the Southern Isles and this made him go desperate to marry into monarchy, thus Frozen's plot.
He has a strong resemblance to Tangled's Stabbington brothers, and it's not an easy thing to do. The hairdo raised the specultions apparently. The conclusion was that the Stabbingtons are actually one of his 12 brothers who are also aware that inheriting the throne is kinda impossible and traveled to Arendelle to find their luck, so we got them as thieves in Tangled.