OMG I figured out what's happening, and I'm horrified.
If the song in question is available in Apple Music, then that song will be automatically treated AS an Apple Music item and therefore will NOT be able to stream even after being added to the iCloud Music Library, on any device running an OS older than 8.4.
So to be clear... music that I created myself that is 100% original (say something out of Ableton Live, Logic Audio, etc.) will be able to be streamed to my phone running iOS 8.1.2. BUT (and I just did this myself so I am 100% positive it is correct), say I rip a song myself from a CD (or download the song from any other website, etc.). If I add that song to my library, it will appear as an MPEG Audio File (or aac or m4a etc.) and be able to be added to the iCloud Music Library, but if that song is also available in Apple Music, then it will NOT stream to my phone!
Additionally, (and this is the really horrible part)... if I remove the download from iTunes, and download it again from the cloud, it downloads an Apple Music DRM-encoded file instead!
The old MP3 (or whatever) version is still on my hard drive, but the iTunes reference now points to their DRM-encoded Apple Music version, and it will not be playable in anything but iTunes.
I'd like to believe this is a bug, but I have a feeling it's intentional. iTunes never used to do this, and in my opinion this is pretty nasty... if I hadn't caught what was going on, I could have ended up with a substantial portion of my library all being converted into Apple Music files instead of the MP3s, AACs, etc. that I already have.
UPDATE: I'm on the phone with Apple now and it's confirmed. Apple Music without iTunes Match will not allow streaming of any newly-added and matched content, to any iOS device using iOS prior to 8.4. Also Apple Music will always replace any matched songs (even if you ripped them yourself from a CD) with DRM-encrypted versions, should you ever download them from iTunes Cloud (paying for iTunes Match would prevent this). So basically it's $25/year to remove DRM for good from non-Apple Music files.
I'm amazed I didn't run into this when I investigated using Apple Music in the first place. I understood that music I actually download through Apple Music (as an Apple Music AAC file) would be DRM, but to lock down my own CD rips if I ever need to download them again!?!? Brass balls Apple. Brass balls.
No - you'll want to find a spare iOS device for your father's account to log in and accept the invitation. (or backup / wipe / set up your device for him - then wipe / restore your backup so that you don't mix streams of data signing out and then signing in as his account).
This would clearly be a bug and something you might be able to call Apple Support to see if they can push an alternate way to authenticate your father to the group.
My guess is the account is either blocked and needs apple push notification to tie it to a physical device one time and then it will work from windows. I've done this a handful of times for people that primarily are on Windows without needing to engage official support.
Best Answer
You can definitely listen to Apple Music on multiple devices simultaneously.
(In fact, my Homepod, Apple TV, and iPhone have an annoying propensity for all trying to play songs at the same time, instead of controlling one-another.)