Ok, so we have established that the overall discount is correct. In your example, these are the numbers:
Product: 117.61
Discount: 6.65
Tax: 15.29
Total: 126.25
The discount has also tax included.
Discount no tax: 117.61*.05=5.88
Discount including tax: 5.88*1.13 = 6.65
What you want is to remove the tax amount from the discount and subtract it to the Tax total
Product: 117.61
Discount: 5.88
Tax: 14.52
Total: 126.25
In order to do that you would have to make modifications to the template.
Using the default virtuemart template, in
www/components/com_virtuemart/views/cart/tmpl/default_pricelist.php, you have these lines of code:
<?php
echo $this->currencyDisplay->createPriceDiv ('salesPriceCoupon', '', $this->cart->pricesUnformatted['salesPriceCoupon'], FALSE)
// can be altered to
echo $this->currencyDisplay->createPriceDiv ('salesPriceCoupon', '', $this->cart->pricesUnformatted['salesPriceCoupon']-$this->cart->pricesUnformatted['couponTax'], FALSE)
?>
And for tax, since you are using taxbill, you would look in the foreach loop
<?php
foreach ($this->cart->cartData['taxRulesBill'] as $rule) {
?>
Where you will find
<?php
echo $this->currencyDisplay->createPriceDiv ($rule['virtuemart_calc_id'] . 'Diff', '', $this->cart->pricesUnformatted[$rule['virtuemart_calc_id'] . 'Diff'], FALSE);
// which can be altered to
echo $this->currencyDisplay->createPriceDiv ($rule['virtuemart_calc_id'] . 'Diff', '', $this->cart->pricesUnformatted[$rule['virtuemart_calc_id'] . 'Diff']+$this->cart->pricesUnformatted['couponTax'], FALSE);
?>
That should do it. You would probably have to make the modifications in your template file
www/templats/[your-template]/html/com_virtuemart/cart/default_pricelist.php