Is there a way to always have parent_tag to be parsed first?
Doesn't look like it. But why would you want to?
E.g., maybe you're inserting parent/child records into the database, and in order to maintain referential integrity, you need to insert the parent records first. Assuming that all parent-specific data is available in the attributes of the parent tag, this would be possible with a start rule on the parent tag. That's one reason why I might want to...as to why the OP wants to, I wouldn't know :-)