Expression to set position of text layer base on a different text layer

The approach to this kind of problem is to tie the position of text layer 2 to text layer 1 with an expression that looks at the position of layer 1 and calculates the true position of the text block in layer 1 using sourceRectAtTime() and then uses the left, width, top, and height as well as the sourceRectAtTime() properties of the text layer 2 to adjust the position of layer 2 while compensating for baseline shift (top + height) and paragraph justification (left and width). You only need an expression for Laye2, and I would use thisComp.layer(index - 1) instead of the layer's name in the composition. You have to do the math so the second layer goes where you want it to go, plus a bit of padding. 

Try something like this to make layer 2's baseline line up with Layer 1's baseline and position Layer 2 to the right of layer 1.

L2 = sourceRectAtTime();
L1 = thisComp.layer(index -1);
pad = 30;
p = L1.position;
s = L1.sourceRectAtTime();
x = s.width + s.left;
y = s.height + s.top;
p + [x + L2.left + pad, 0];

As long as you have not fiddled with Baseline Shift and the second text layer, Paragraph justification is set to Left, that expression should keep things lined up and both layers at the same level.