The first answer is yes, there are probably hundreds of these devices out there. [A lot depends upon the range and the SIZE needed.] You can buy they in sets if you want, keyfob and a little RF receiver/decoder PCB. The receiver has the ability to set a "code" and if it is set manually (i.e. you set it yourself) then there is no problem with setting two receivers to the same FOB code.
Latency of < 1 second... Piece of cake.
Simultaneous triggering < 1 ms. That's going to be the problem. These things work in the unlicensed band, usually 315 MHz. Lots of noise, lots of multi-path reception. When you press the button on the FOB it just starts sending out a train of data packets, over and over. The idea is that eventually ONE of them will get through intact. The data rate is slow, and there could be 50 to 100 ms or more between the start of one packet to the start of the next. Your problem - one receiver will almost certainly see a valid packet that the other one missed, causing the second one to trigger on a latter packet. At close range this probably won't happen (often), but at longer ranges (like 100m) it almost certainly will, very often.
I'm not sure of a good solution to that (one that isn't too involved). If I were to pick a starting point, I would pick a receiver that has an RF Signal Strength output (lots do, but not all). I would then trigger not on the reception of a valid START packet, but rather on the loss of signal FOLLOWING reception of a valid start packet. That would probably work, but you would have to run some tests to see how well it works in your specific situation. [In your living room, probably great. In a factory filled with heavy electrical machinery... probably not so great.]
If you are looking to buy COTS, you might also look at the little rigs that photographers use to trigger remote flash equipment. That would seem to be very close to your requirement (except maybe for range). If you are looking to design and build custom - look at the Micrel "quick radio" chip sets.