The mosaic is 1/4" thick, the porcelain planks are 3/8" thick. What's the best way to install?
I'm thinking I need to build up the floor where the mosaic will sit. I could use uncoupling membrane -- put 1/4" plywood on subfloor where mosaic will sit then cut membrane to fit the 2 different thicknesses. Or use backerboard, and build up where the mosaic will sit with something on top of that, but what -- more cement board? Uncoupling membrane? Some kind of underlayment?
1/8 inch is not a big deal. There is no need to build up the floor under the tile.
If you use a 1/4 inch notched trowel to apply your thin set and tilt it at about 45 degrees your thinset will be just slightly higher than 1/8". Use that method to set your plank tiles. Then apply thinset with the 1/4" trowel at 90 deg. to the floor. You now have thinset that is higher for the mosaic than used for the planks.
Lay the tiles and compress them slightly into the thinset, as you always should, and the height will come out within a fraction if not exactly to where you need to be.
Your could lay down an uncoupling membrane and then apply the thinset with a 1/8 V-groove trowel. This could work too, but you have the additional step.
Remember a slight variation in height (1/16-1/32) will not be noticed by your feet, ( or your eyes). The variation in the stones are excellent in compensating, especially after being grouted.
I think you'll have a challenging time simply trying to leave more mortar with your trowel in those areas. 1/8" doesn't sound like much, but it's enough that you need more mortar volume than a simple trowel tilt will leave.
I would back-butter the mosaic tiles with the same trowel, essentially doubling the mortar volume. Adjust as needed. Pay close attention to the edges so that they're well supported.