Iain,
for radio buttons to work correctly they must be named the same so change your code to look like this:
<p>
<label><input type="radio" name="VehicleType" value="Car" id="VehicleType_0" class="tickbox"/> Cars</label>
<br />
<label><input type="radio" name="VehicleType" value="Van" id="VehicleType_1" class="tickbox"/> Vans</label>
<br />
</p>
and then change your code in the Data Assist Search from this:
$WADbSearch1->addComparisonFromCheck("Category","VehicleType"," Car","","AND","= ","=",0);
$WADbSearch1->addComparisonFromCheck("Category","VehicleType2", "Van","","AND"," =","=",0);
to this:
$WADbSearch1->addComparisonFromEdit("Category","VehicleType","AND","=",1);
I use radio button searches a lot in the admin panels that I build and this way of doing things has always worked for me so give it a go and see how you get on.