Pugwinkle I copied this from the regular Echo forum.
I also bought two Echo Shows to help me communicate with my elderly mother on a daily basis. Like you, I set up an amazon account for my mother. (Note: a prime membership is not necessary to access the basic features including video calling.) The only hitch may be setting up wifi access once your parents have the device. It is super simple to do (as you'll see when you set yours up on your own home wifi) but it does require knowing the wifi password. If you know it, then you can easily talk them through the steps on the phone once they receive the device.
Here are the steps I took to set up the devices and enable video calling:
First - login to your amazon account and deregister the device you'll be sending to your parents.
1) Plug in and turn on both Echo Show devices and connect them to your home wifi. Get them started updating. (It took mine about 10 minutes to complete updating.) It is best if you set them up in separate rooms as far away from each other as possible - this will make testing out your set up easier later.
2) Install the Amazon Alexa app on your phone.
3) On a computer (not your phone), set up an Amazon account for your parents. It is helpful if you use an email account to which you have direct access. Be sure to make a note of the login information you create - you'll need to use it several times.
4) On your phone, login to your Amazon account on the Alexa app. It will immediately ask you to enable calling and messaging. Follow the prompts. You will need to enter your cell phone number in order to receive a text message to verify that you do in fact control that number. The app will ask to access your contacts in order to determine who you can call from your device and your app. (It compares the phone numbers in your phone's contacts list to phone numbers associated with an Echo device; those are the only contacts that show up in the Alexa app.) For me, we have multiple echos in our household, so I enabled "drop in" for my household only. Drop in is the Alexa feature that allows two Echos to connect with two-way audio or video communication (depending on the device being used) instantly. This is different from calling to an Echo device; initiating a call to an Echo requires the person you are calling to verbally accept the call. Drop in is the only way for multiple devices registered to the same Amazon account to communicate with each other. You can also allow other contacts outside your household permission to Drop In on you. I set my mother's Echo Show to allow me to Drop In on her because she would become confused by the calling feature but I did not enable her to drop in on me.
5) After you finish setting up your Echo device on the Alexa app, LOG OUT of the app. You access the log out feature through the settings menu - scroll all the way down and you'll see a button at the bottom of the settings list to "Sign Out". Once you've successfully signed out, close the app and then re-open it - THIS time, sign in using your parents amazon account that you just created. This is where you may need your parents on the phone with you because you're going to enter their cell phone number into the app this time. Like before, it will send a text message to that phone number and you'll need to enter that code into the app to prove you control the number. If your parents can text, that shouldn't be too confusing for them. If they cannot text, then perhaps a friend living near them can be there when you call to help them find the text message. Now, here's the tricky part - because you are using your phone to set this up, your parents' device will show the same contacts that you have. As long as you are listed as a contact in your own phone, this shouldn't be a problem - you will show up as contact for them and you can always block any of your contacts you don't want to be able to call them. Alternatively, you can temporarily remove those contacts from your phone before doing this step so they just won't show up on their device at all. This is in fact what I did. (Each time you login to the Alexa app, it updates your Alexa contacts from your phone contacts so when you add them back into your phone and login to the Alexa app as yourself, they will show up again.) Set up the permissions the way you want them on your parents' device - Drop In, etc. When you're finished with all of that, LOG OUT of the Alexa app and close it.
6) Re-open the Alexa app and login with your own Amazon account this time. You should now see your parents as a contact. Set things up the way you want them for yourself.
7) Now you get to check to see whether it's working! Go to one device and try to initiate a call to the other. For me, it worked pretty instantly. You can play with them and adjust settings so it's easier for your parents. (My mother won't be able to adjust anything so I made it as simple as possible.)
As a side note, if you are a prime member and use Amazon photos, I think it's possible to share the Family Album with a non-prime account; that may allow you to set up the screen saver on your parents' Echo Show to display your family pictures. (I haven't done this yet which is why I am not sure about it.)
Good luck! I puzzled over this for a few days before finally landing on this as a solution.