I used to have a couple splitters for this exact reason. I like to watch live sports synched perfect in living room, kitchen, and back patio.
I have since upgraded TVs. The old splitters no longer work. Bought a new splitter, worked for awhile, then stopped working.
I asked the local A/V pros, and basically, the (weak/unfortunate) answer is that different TVs work different/funny with different splitters and cables. The only way to know if they work is to try them. I had to try several initially to get it to work. It has been on my "to-do" list for some time now to find a new one. I ran the cables up my walls and across the attic. Just need a new splitter now to make it work again. It is odd, because a particular splitter may work for a few moments or minutes, then just drop out. Best I know you just have to experiment.
Good Luck! Please share results if you succeed!