You don't have to take the image down if someone later has issues with whoever else they had put into a commission. That would be, in effect, taking away your ability to advertise yourself and losing the potential revenue from that. But their issues are their own and they had no business involving you once you declined and explained the fee (which is perfectly reasonable). Along the same lines as if you were to get a tattoo of your name and your SO's name encircled with flowers or something on your arm--if you later had a bad breakup with that person, you can't just go to the tattoo artist and throw a hissy fit and demand they remove/retouch the tattoo for free. You have to pay for that service. (Though tattoo removal uses time/materials that not posting or taking down an image online doesn't, but in both instances the artist loses an avenue of advertisement and your personal relationships are still none of the artists' business.)

So, to answer your question of if you handled it properly, in the first instance yes, in the second with the SO involved I'm not sure, depends on if you have the 'no showing off' fee in your TOS. But I can understand why you did what you did and if it ended that situation then it's water under the bridge by this point. Just take this situation as a lesson learn and make sure you have something related to this in your TOS for the future.