I think I have the answer (maybe?). I suggest anyone who has had problems with cancellations and refunds with OGF call the Archives.com billing department directly at 888-896-4442. Archives does the billing for OGF.
On May 8 I signed up for the free trials for both Archives.com and OneGreatFamily.com but saw right away they didn't have what I needed. On the same day I cancelled both, saw the cancellation emails but only opened the Archives one. I assumed the OGF one was cancelled as well.
Today, May 24, I got my credit card statement and saw OGF charged me for the full year. I went back to read the cancellation email and saw I should have clicked on a link to complete the confirmation. I did that then saw I also had to call the cancellation department to complete it.
I called and was told I would have to call Archives billing about a refund at 888-896-4442. I did that and was told they would issue a full refund by the end of the day, send a confirmation email and it should take two or three days to see the refund on my credit card. He said he would also contact OGF to cancel my account and stop further billing.
I think OGF is feeling the hurt from all the complaints against them. The woman I spoke to in the cancellation dept sheepishly gave me the information I needed and the biller at Archives was super nice and had no problem giving me the refund.
Hopefully, all will go as promised and, if not, I'll protest the charge with my credit card company.
Good luck, everyone.