I managed to nab a [item=30% discount card] from the free shop. I had a 20% locked in my inventory unlocked it even moved it to my vault and have shopped but it hasn't hit. Now my 20% one won't even work. There's no option I see to "activate". Am I missing something?

You don't need to do anything to "activate" a discount card! You just need to keep it in your inventory. And then when you buy something from a main shop you should see a message like this when you purchase something: I see you have a discount card! I'll give you a discounted price of 1,481 sP!

I have bought numerous items and the only one that pops up is the event one for 15% off. It doesn't seem to catch my 20 or 30

The message should say something like this

The first line references your discount card and the last line (highlighted green) references the buff. The discounted price number should work out to be the correct total with both discounts

You also can't use both a 20% and 30% discount card at once - you're best off selling the 20% discount card.