I figured it out for myself. The series is Shadow of the Dragon by Kate O'Hearn, it is a two book series, and oh boy did I forget the entire plot. My child self must be ashamed of me.
Summary of Kira:
Kira is twelve and strong willed. The daughter of a retired dragon knight, she yearns for adventure and dreams of following in her father’s footsteps astride her own magnificent mount.
But this can never happen. According to the laws of the kingdom, all girls must be married by the age of thirteen. Kira hates it, but being a girl, she has no choice.
When war comes to the kingdom, Lord Dorcon and his knights arrive at her home to take her father, mother and brother, Dane, to the palace to serve the king. Kira and her sisters are to go to Lasser Commons – the most notorious prison in the land. Their only crime? Being unmarried girls.
In a whirl of destruction and fire, Kira and her younger sister, Elspeth, manage to escape. But deep in her heart, Kira knows the real fight is just beginning. She and Elspeth are on the run and being hunted down by Lord Dorcon. When they are caught, they are to be executed.
To stand a chance ever seeing her family again and to protect the life of her younger sister, Kira will need every bit of will power she can find.
Let the battle commence…
Summary of Elspeth:
One day, a young girl astride a twin-tailed dragon will destroy the monarchy and change the world for ever…
Kira and Elspeth have already broken FIRST LAW many times over. Now outlawed and running for their lives they are determined to stand amongst the men and fight the unjust FIRST LAW that binds the kingdom. But cruel Lord Dorcon still stands in their way and the heat of his chase is stronger than ever.
Strong and determined, Kira has done all that she can to protect and shield her younger sister. But now it’s time for Elspeth to grow up. When Paradon’s muddled magic separates the girls and sends them travelling through time to different eras, new challenges and terrifying threats await the sisters. Especially to Elspeth, left all alone to navigate a past world long before the rule of King Ardon and FIRST LAW. And all the while in a strange, alien world of the future, Kira must find a way to get back to Elspeth and reunite her family once again.
A prophecy to fulfil. A cruel monarchy to upend.
The battle continues…