What word or phrase could describe the reaction one has to a bad joke/pun that they actually find funny?

You had the answer at the tip of your tongue: humoring. When you hear a bad joke--maybe even a horrible opinion, a stranger's conversation starter, a boss's reprimand--then you humor that person by giving the expected response (a laugh, a nod, a smile, a sorry expression) even if your heart really isn't into it. Humoring is used as a verb.

So instead of a reaction, try to frame your thought as an action: "I humored dad when he started the knock knock joke by making sure I would laugh at his punchline, whatever it would be."

I'm afraid "Humoring" won't do. That is what you do to get along with the joke teller. To stall and move the situation to some other subject.

Unfortunate is the description of the joke and your reaction. When you actually find the distasteful joke funny, and laugh, despite your knowledge and sophistication it can be politely called Unfortunate. Meaning that it's really too bad, shameful in fact, that it is so funny since it is truly unforgivable in its humorous power. This incorporates the begrudging respect/admiration you mentioned above. We must keep a respect for humor, begrudging or otherwise, if we are to survive.

That joke was so bad that I laughed despite myself.

How about in spite of? From Lexido:

in spite of: Without being affected by the particular factor mentioned.

Example:

I laughed at my Dad's joke in spite of how bad it was.

In spite of implies that you recognize how bad the joke is but you can't keep from laughing at it anyway. Your positive reaction is not affected by the joke's recognized badness.