Light help

In my kitchen I have 2 lights that seem to be on 2 different circuits one switch at each end of the room when I turn one side on the other side goes on ! And vice versa. (Not sure of the term)
I want to add a outside light(led 30w) for the rear of my garden and hoped I could piggy back off the switch at the back of the kitchen and add a switch/power for the outside light.
This simple/terrible diagram shows the lighting situation .
Any electricians on here can tell me if I can even do what I wanted to do ? I have had a try and obviously when I try and piggy back off the switches the kitchen lights turn on/off.
Any help is greatly appreciated
Thanks

You needed to establish a neutral connection. Everything does not work as you intended because you initially made a mistake in the chain. It's a good thing you didn't set fire to anything. Otherwise, the situation would have been entirely different. I hope you have already connected it. I recently had another problem. I bought a standard lantern for my son's flagpole at a hardware store near the house. And it started flashing just a week later, as my son told me. Then it was raining, and I already thought that I had not made insulation everywhere...But it turned out that it was the light bulb itself. My son has already bought himself an LED flashlight. I'm sure it will definitely hold more than the previous one. He purchased it here https://www.amazon.com/Flagpole-Energy-Battery-Illumunation-Vont/dp/B00YBDA7DC/ . Now we don't trust that hardware store.