No, you should not be paying the tax twice on the same trade.
If you used the vehicle 100% for those 2 businesses equally, then when you report the sale on each business you will enter only half of the sale price. Or if you used it 70/30, you would allocate the sale price 70/30.
If you had personal use of the vehicle then you would allocate the sale price between the two businesses and personal.
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