You need to do the relative_time(datefield,"@d") on both sides of the lookup.
Also, there's a basic issue you might run into with "it's the Fourth of July holiday WHERE"?
The records are stored in UTC, (which we'll pretend for the moment is London's time zone.) If a user is viewing the search in, say, San Francisco, then the interface may choose to determine what date/time the record occurred in San Francisco, or might not, depending on how the search and the system are set up.
So, if converting the other dat field doesn't do the trick, then before you do any more the conversion and testing in the above search, you need to determine precisely how the data is stored and precisely how the system is interpreting relative_time( sometimefield,"@d").
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