It sounds like you've given the Search module an earliest and latest param such that that module itself specifies a timerange of last 7 days.
If this module is downstream from the TimeRangePicker, then indeed, that hardcoded timerange will override the TimeRangePicker's timerange.
I would remove those earliest/latest params from the Search module, and instead put <param name="default">last 7 days</param> into the TimeRangePicker itself.
The Search module can certainly prepopulate timeranges in TimeRangePicker, but only in cases where they are upstream from the TimeRangePicker.
UPDATE - short version -- for the Search module (or the legacy HiddenSearch module) to inherit it's timerange from an upstream TimeRangePicker, it needs to have no "earliest" or "latest" params itself.
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