first of all, is she using her own account or sharing yours? Hopefully it is her own account. If yours, you really do not want others to access your info. Never know if a visitor, whether caregiver or friend may try to abuse it.
Youtube has always been flaky when it comes to echo devices. Maybe download the church service then upload it elsewhere, check out ibroadcast. It is a free cloud service for media content and it works with alexa.
For other family members, as long as they log into her alexa account, they can specify which device to to play stuff on. For example, you can command alexa on your phone to play church service on her show. just use the name of the dot as part of the command.
Need clarification, are you wanting the show to play the church service video but the sound on the dot? If so, it cannot be done but you can group the two together and it will play on both.