What you currently have is most likely two switch loops. On both sides, the power is first arriving at the load (outlets or lights), hot, neutral and ground. The hot is spliced to the black wire going to the switch. The white to the switch is the "switched hot", returning from the switch to the load. Technically, the "switched hot" white wire should have a loop of black tape or paint at the ends bug many people skip this.
The easiest thing to do is, at the switch for the outlets, disconnect the wires from the switch and wirenet them together. This will make the outlets always hot. If you'd prefer, you can find the other end of this cable, disconnect both ends, label them "abandoned", wirenut the ends and stuff them back into the boxes. At the outlet, connect the now free wire to the outlet where the switched hot was connected originally.
At the other switch box, you have the hot and switched hot. Connect these to your three-way switches and new cable.
Edit: the three-way wiring should be as follows: incoming hot to switch 1 common. On your new 14/3, connect black and red to the switch 1 switched terminals to act as travelers and connect white to the incoming white as the returning switched hot. On switch 2, black and red travelers connect to the switched terminals and white switched hot to the common terminal.
In this arrangement, switch 1 switches hot between the two travelers. Switch 2 switches between the two travelers to provide switched hot back to the load through the box containing switch 1.
Don’t forget to add a black mark to the ends of each white wire to mark “switched hot”.
Edit 2: here's a diagram of what I wrote above:
Note that grounds are not shown. Connect them appropriately.