SSH is not HTTP, so discussion of your website is not relevant (and yes, passing http:// to ssh will confuse it).
When you say "mapped to", I don't know if you mean that:
- melikecandycoveredfrogs.com is an A record pointing to 18.104.22.168 (assuming 22.214.171.124 is your IP address)
- melikecandcoveredfrogs.com uses a META REDIRECT to direct the browser to http://126.96.36.199
- You have an A record "myip" pointing at 188.8.131.52, and melikecandcoveredfrogs.com is a CNAME pointing at the "myip" record
- You're doing some kind of NAT or portforwarding on the machine that melikecandycoveredfrogs.com points to in order to direct traffic to the myip machine
The first and third should work fine, the second won't (ssh is not http, your ssh client won't understand an HTTP redirect).
The fourth option could potentially work; if you've remembered to forward port 22, if you've used the appropriate combination of DNAT and SNAT
Can you post the output of "ssh -v melikecandycoveredfrogs.com" (with hostnames/usernames/IPs altered) so we can see what's going wrong?
 DNAT will always be required.
If the return traffic from myip back to the source of your connection passes through melikecandycoveredfrogs.com on the way, melikecandycoveredfrogs.com gets a chance to do the required NAT on the way back out as well.
If the traffic doesn't normally pass through melikecandycoveredfrogs.com though, you'll end up with your source machine making a connection to melikecandycoveredfrogs.com and getting a response from myip, which is going to confuse your source machine, and it will just drop the confusing packets.
In this case, melikecandycoveredfrogs.com will need to do SNAT as well; so that myip thinks the connection originated from melikecandycoveredfrogs.com and sends the response back there; melikecandycoveredfrogs.com can then rewrite the addresses and send it back to your source machine.
I'm fairly sure this isn't your problem though, as http connections would have the same problem, and the way you've asked your question implies that http is working fine.