Update: Looks like points.com directed Icelandair to close my account:

Ryan: Hi, welcome to Points.com Live Chat, how may I help you?
You: Hey Ryan- About a month ago I bought some Icelandair miles, but using my husband's credit card. The transaction ended up getting cancelled for some reason, and then I couldn't login to my Icelandair account. I contacted them & they told me that points.com instructed icelandair to close the account.
You: I'm trying to understand why and what happened to my miles that I paid for?
Ryan: I would be happy to help you with that.
Ryan: One moment please while I check your account. Do you mind holding?
You: By all means
Ryan: Still checking, I appreciate your patience and holding on.
Ryan: I can only confirm that our auditing team did ask Icelandair to close your account.
You: Ok, why though? I can provide copies of our ID's, marriage license, etc? Why was it closed without notifying me?
You: How do I get my miles or money back?
Ryan: I am afraid that I will have to escalate this issue as it is beyond my authorization level.
You: Please do. Right now I've paid for something I haven't received
You: Is there a contact at points.com I can reach out to?
Ryan: I have escalated the issue to our auditing team as they are ones who would have requested your account closed.
You: Ok, is there someone on your auditing team I can contact directly?
Ryan: I'm afraid not.
You: Ok, thanks for your help.
Ryan: I will contact you if there is any news on this front.
You: Please do, I have done nothing wrong, I don't understand why you would have closed my account after spending over $650 with your company
Ryan: I will. Thanks for chatting today.

Now, what is the best approach to bring these people to small claims court? I seriously doubt they'll respond at all.