Hey perapera,
That diagram you gave looks like exactly what you want if the pressures are in the right range. I think it is possible that you are confused in how to read it. I attached an example- hopefully I got this right.
Find your initial (liquid) composition on the x-axis. Run vertically to the liquid line at your pressure and read the temperature off the y-axis. This is the bubble point temperature, which we commonly call the boiling point of the mixture. The composition of the first vapor generated is found by reading the x-axis value for the corresponding vapor line at the same temperature. This first vapor is essentually pure water for a starting mixture of more than 20% water.
The same approach (but going to the vapor line) can give you the dew point, and composition of the first liquid formed. In between (the 2-phase region) you can get the vapor and liquid composition at any temperature. The starting composition does not affect the phase compositions, but does determine how much of each phase is present- you can use the inverse lever rule to calculate graphically.
Your curves look pretty ideal so depending on how much accuracy is needed, you can probably do the flash calculations (bubble-T, dew-T, or general flash) using the pure component boiling points, and Raoults law. It is worth a quick try to compare against the diagram.
best wishes,
sshep