Avis has a Sony LCD TV and she says that she's having trouble connecting her Bluetooth speakers and home theater to it. They work with her tablet and mobile phone, but not her Sony TV. Leo says that Sony doesn't put the A2DP Bluetooth profile in the TV OS (although this year's models do). That's probably why it can't pick it up. Also, only one device can connect to Bluetooth at a time. So she can't have it do double duty.
Leo says that if she wants multiple connections, then Sonos is a better option. They have a special setup that can do multiple Bluetooth sources. That's closer to what Avis is looking for, but they aren't cheap.
Another option is Google's Chromecast Audio.