Trying to figure out this wiring
I have pulled both switches out and at the end of the room with the three way switch I found that it has the standard setup for a three-way; one white, one black, and one traveller. 


A standard three way setup has a hot feed or a switched leg to the load, and two traveler wires between the two switches. One switch gets a hot feed and the other gets the switched leg to the load.

The "two-way" switch you describe is a single pole switch and does not belong in a three-way switch loop. That is why the circuit does not work properly.

The problem with giving you a diagram is, there are several different ways to wire this circuit depending on where you feed the circuit. So, you need to determine where the circuit is fed from. The light or one of the switches are your choices.

Search the interwebs for "three-way switch circuit" and you should be able to find all of the several iterations of this circuit.

Good luck!