Use the “watch party” feature on prime video.

Caveat: I haven’t done much testing with this and haven’t used it beyond two TVs or Amazon prime video yet, this could potentially work with more TVs and other streaming services. 

I’m on mobile please forgive typos, and formatting.

I started the watch party on the TV in my kitchen, then used an alternative profile on the same account and just connected via the QR code it displays and it just popped up on my other TV. It was surprisingly much easier than I thought it would be, and worked instantly; there’s only a minimal amount of latency.

Additional protip: start the host TV from your alternative profile on the account. I think this matters so that when you scan the QR code, it’ll automatically pop up on your main account. 

Also, when you pause on one TV, it pauses all the TVs except for the host I think. I just figured this out last night so I don’t know all of the details, but I figure other people would like to know about this.  I had previously searched for a solution for this situation, and only had seen clunky hardware suggestions.

Anyways, I hope this helps you and I hope you have a great day ! ☺️