How to make a slotted assembly slide together?
When you add your mates, you can use advanced mates rather than standard mates.
I started by selecting the right planes of your outer slot and middle slot.
Under the advanced mates tab, select the distance icon (the number next to this is the current distance between the two planes). to get the freedom I think you are looking for I made the maximum value 3.5 and the minimum value -3.5.
I then repeated the steps matting the right planes of the middle slot and the inner slot.
I used the same values and after you click the green check you should be able to move your assembly the way you desire.