How to deal with SP Apps when the SP farm is in a different AD domain?

I have a situation here where my laptop is on our "production" AD domain, and my SP2013 farm is in a "test" AD domain. I have a personal account in the test domain, and I have set up a generic SP Admin account in the test domain. (My personal account is also a farm admin and site collection admin.)

I have set up the app infrastructure correctly (app domain in DNS, etc.), and apps seem to work, but I was running into the issue of the app config page and app parts prompting for credentials. So I followed the advice I found online and added the app domain to my local Intranet sites in IE internet settings.

Now what's happening is that the app parts and app configuration pages say

Sorry, this site hasn't been shared with you.

I'm logging in to my laptop with my production domain credentials, but when I go to the SP site I'm logging in with my test domain credentials. If I take the app domain out of my Intranet sites, and force the second credential check, and use the test domain credentials, everything seems to work. So I'm guessing that what's happening is that with the app domain in the Intranet sites, my production domain credentials are getting passed on to the app.

Am I right in my assumption? What's a good way to deal with this? I've had previous experiences that led me to believe SP would use the credentials you logged in to the site with (in this case, my test domain account), which are associated with the browser session, and not default to the credentials you are logged in to the machine with.

Edit:

In addition, it seems like anything opening from the app domain loses all the SharePoint bits. Here's a screen shot of an app configuration page in a working environment:

And here's a screen shot of the same app configuration page in my environment:

Anyone have any ideas as to why this might be happening?