Could you go in the menu Display->Views and edit the file shipping of the view checkout ?
There, change the code
to
if(bccomp($taxes,0,5)==0){
That will display the taxed price when a tax is applied to the shipping price on the shipping selection view.
Then, in the same file, change the code
echo $this->currencyHelper->format($rate->shipping_price_with_tax,$rate->shipping_currency_id);
to
echo $this->currencyHelper->format($rate->shipping_price_with_tax,$rate->shipping_currency_id);
echo JText::_('PRICE_BEFORE_TAX');
echo $this->currencyHelper->format($rate->shipping_price,$rate->shipping_currency_id);
echo JText::_('PRICE_AFTER_TAX');
That will display teh price of the shipping methods like this:
My shipping method 1 17,76 € (14,85 € without VAT)