I am able to access the first raspberry pi listed below through the Linux Remote Desktop Viewer: myhost.mywire.org

MAC Address b8:27:eb:fb:97:4f
IPv4 Address / Name 192.168.1.64 / raspberrypi
. . . . . . . . . .
I have tried to access "raspi2" below using myhost1.dynu.net. However, it does not work. It takes me to the same computer as myhost1.mywire.org.

MAC Address b8:27:eb:15:68:af
IPv4 Address / Name 192.168.1.85 / raspi2
. . . . . . . . .
Both raspi's are at one IPv4 address.
Should the address be followed by a ":" and another number to distinguish between the two machines?
I am stuck until I know more.
Sincerely

As you don't say how you are accessing them (SSH, HTTP etc) I'll take a guess that whatever protocol, you are port forwarding and unless you have setup two different ports (i.e. one non standard at least) your router/Firewall will also send the inbound connection to the public IP address to the same Pi.
You will need two different port forwards and too some extend it doesn't matter which domain name you use, as they probably both resolve to the same public IP address anyway :-)

I was having the same problem, I don't know if this is the right way but it works for me:
First I set up the port forward for each pi:
pi1 external 80 pointing to internal 80
pi2 external 8022 pointing to internal 88

then created an alias for my first pi: pi1.mydoain.com and for pi2 I created a redirect: hostname pi2.mydomain.com destination http://my.ip.adress:8022 and now it works fine.
Hope that helps