Since it appears that you want to listen to either DTV or Music System [i.e. AVR, Sound-Bar, or HTIB] I'm going to PRESUME that "PLAN A" would be to connect Digital Audio (Optical) Output on DTV [most have it] to Optical Input on Music System.
I would advise AGAINST using Bluetooth for Front Speakers since it uses lower Quality COMPRESSED Audio and has short range limitations. If you decide to use a WISA, Wi-Fi [or Bluetooth] Audio Extender (see below), then you would presumably connect Audio OUTPUT of Music System to Audio Extender Transmitter via one of the Music System's OUTPUTs [e.g. Optical, Speaker Output Terminals or Pre-Output RCA Jacks]....which varies depending on which of the following approaches is selected.
"PLAN B" would be a separate approach which would operate independently of the Music System and hence would presumably need an A/B Optical Switch to select either DTV or Music System as the Source.
FOLLOWING ARE ALTERNATIVE APPROACHES:
1) Many HTIB Systems have Wireless Speakers...but ONLY for the Surrounds and maybe LFE....NOT for the desired L/C/R speakers. And some AVR's transmit Bluetooth [COMPRESSED audio, Short Range, Line-Of-Sight Limitations]...but read the fine print, since AVR contains the High Power Amps, it likely only supports L/R to Headphones....and/or LFE and/or Surrounds.
2) OTOH: Over the past several years, a NEW Wireless Technology has begun to be available to overcome the Range and Sound Quality limitations of Bluetooth, called WISA (WIreless Speaker Audio). See list of mfr's [incl. specific models listed below] who have adopted WISA [in 5.2-5.8 GHz Band, mostly BELOW the 5.8 GHz Wi-Fi Band] for distributing 5.1/7.1 Digital Audio Signals in UNCOMPRESSED, up to 24-bit, 96 ksps Digital Audio Formats:
Enclave CineHome Wireless Theater has [long range] Wireless Speakers for ALL SIX...even the L/C/R, so you are free to locate ANY of them anywhere you want:
Enclave Audio CineHome HD 5.1 Wireless Audio Home Theater System | Wireless Speakers Shop
Axiim Q is another ALL Wireless Home Theater System...unfortunately Amazon only has WISA Speakers still in stock:
[$2500 for 5.1 and $2900 for 7.1]
[Review of Prototype]
Some (All???) of the fol. Klipsch Systems use WISA for Wireless Connection to Some (All???) of the Speakers (I didn't check each model):
3) Fol. SoundCast Wireless Speaker EXTENDER/AMPLIFIER System has a long-range Wi-Fi TRANSMITTER that connects to [ANY] Music System's L/R FRONT Speaker OUTPUTS [Optical NOT supported] and sends Wireless Signal to the RECEIVER, which has a BUILT-IN 2x50 W/Ch STEREO AMPLIFIER to drive a pair of connected SPEAKERS [ANY Speakers....could continue to use EXISTING]. To listen to DTV, the Extender's Optical Output would be connected to one of the HTIB Optical Inputs [PS: DTV's do NOT (yet) provide an HDMI OUTPUT]. Obviously, the Receiver must be plugged into AC Power and has wires to L/R Speakers:
https://www.amazon.com/Soundcast-SurroundCast-Wireless-Receiver-Transmitter/dp/B003F7R7SI [2.4 GHz Wi-Fi, 2x50 W/ch Amp]
4) There are LOTS of Bluetooth Enabled Speakers on the market....most of which are JUNK....and are LIMITED to SAME ROOM, mostly Line-Of-Sight Operation...which may or may not meet your needs. Here's one that didn't seem to fall into the "Junk" category....I'm sure that there are more to choose from:
If you don't have a Bluetooth Enabled Music System, you would need to add an Optical (From DTV and/or Music System) to Bluetooth Transmitter, such as:
This particular Bluetooth Transmitter ALSO comes with a Bluetooth RECEIVER, each of which could be plugged directly into ANY Amplified Speaker (too numerous to pick out any favorites). It also claims to be LOW-LATENCY so hopefully no LIP-SYNC problems and has a USB I/F Cable that presumably can be plugged into DTV to provide round-the-clock power to the device...or you can get a small Wall-Wart with USB 5VDC Output.
5) Fol. Long-Range, CD-Quality, Wireless Sub-Woofer/Surround Speaker Extender is pretty simple and can be used with ANY Powered Speaker. The TRANSMITTER is designed to plug into the SW [or Surround] RCA Output Jack(s) on a Music System [if so equipped], with the RECEIVER connected to thee RCA INPUT Jack on a POWERED Speaker (which only need to plug into AC Power). You would need a TX/RX Pair for each Powered Speaker, beginning with the L/R Fronts. There are MANY Powered (incl. AC or Battery) Speakers to chose from....here are just a few:
6) Wireless Speakers, including a W-L Transmitter (Long Range, NOT Bluetooth):
SMALL, W-L SPEAKER with LOW AMPLIFIER POWER
[Perhaps in ADDITION to Primary L/R Speakers???]:
[900 MHz, Battery or AC]
[900 MHz, Battery or AC]
LARGER, W-L SPEAKER with MEDIUM TO HIGH AMPLIFIER POWER:
[Wi-Fi, Sonos Play-5]
[2.4 GHz Wi-Fi, 20-hr Battery or AC Power, 100 W/Ch]
[Wi-Fi???, AC Power, 80 W/Ch]
[2.4 GHz Wi-Fi, 15-hr Battery or AC Power, 60 W/Ch]
[2.4 GHz Wi-Fi, 6-hr NiMH Battery or AC Power]