Theory: Hash is the Dream Princess' "sister".
Explanation: A woman from the mortal realm and a man from the Dream Realm (presumably the previous faux ruler), were in a relationship, and the woman got pregnant. When the woman woke up back in the mortal realm, she retained her pregnancy. Then one night, she returned to the Dream Realm and gave birth to the Dream Princess. When she woke up, she was still pregnant in the mortal realm, and gave birth to Hash. The doctors in both realms told the woman she was going to have one child, but due to having an interdimensional affair with the man from the Dream Realm, she technically gave birth to twins, one child for each parent. And thus, Hash and the Dream Princess share the same parents and are technically sisters, when they're really alternate versions of the same person.
Is this confusing? Yes. Is it the only explanation I can think of? Also yes.
A few headcanons to accompany this theory:
- Mortals can't have the powers of dream beings, but can gain them when possessed by a dream being using a copy of their sword
- The girls, despite one of them being restricted to her home realm, have a very close and wholesome relationship as "sisters"*
- They both equally care about Quest Sprout
- Hash has been possessed by the Dream Princess before, and is her official vessel for the mortal realm
- The reason their shared sword design is two swords fused together is because it represents their "sisterhood"**
*I imagine the Dream Princess always trying to make Hash feel special whenever she visits the Dream Realm.
**This is something I JUST thought of, as of typing all of this!
If this whole theory is true, it'd be a very cool way to represent families who may be apart physically, but never mentally, like mine for instance; My family is Canadian, and we all live in Edmonton, except for one of my sisters, who moved to Vancouver, and occasionally visits us to hang out for a bit.
This theory also fleshes out the Dream Princess and Hash as characters, and gives them more reasons for being in the series!