what's the meaning of "However touching may be an interest so tender"
Solution 1:
The interest so tender is the supposed intention of providing happiness.
This is seen as a tender thing when e.g. a lover wants to make their beloved happy, but the author has doubts about the real intentions of authorities when it comes to providing happiness.
Touching is "touching the heart", that is, something very nice.
You could rephrase the sentence as:
No matter how lovely it may be that the authorities want to be so kind as to give us that happiness, [...]