I think many people trying to implement this type of design would agree that it is a reasonably complex thing to get right for people not familiar with it. But as with most foreign things, once you get used to the idea then it is not so bad.
I would suggest, as with any complex designs, is to try and break things down into simpler components in the first instance, and as users built more trust and confidence in the system you can ramp up the level of complexity then.
So in this instance, why not break the query down into its components, like you have done visually with the dates and the price. Separate them into physically separate input fields, but design it in a way to show that they are all part of an extended query/search string. That way the user can focus on each aspect of the search input without worrying to much about whether they have structured it correctly, or whether there are context sensitive input that can make interpreting the input and results confusing.