Re: advice sought for design of a search facility for a sub-site

>   <label for="rad1">Online Shop</label>
>   <input type="radio" name="radiobutton" id="rad1" value="radiobutton">

Why didn't you use the implicit form:

<label for="rad1">Online Shop
<input type="radio" name="radiobutton" value="radiobutton">
</label>

The explicit form is only really intended for use where tables separate
the label from the control.  In other contexts it just pollutes the
name space and introduces a cut and paste error risk.