V2 will sink very little current unless there's a load attached (similar for V1).
Your two voltage regulators are in parallel, so their branch currents add (see: Kirchhoff's Current Law).
So if V2 is attached to a load which will draw 0.4A at 1.2V, then that means V1 can draw at most 0.4A regardless of what voltage V1 is set to.
Note that linear regulators (like the LM317) have a drop-out voltage, so your output channels will only be able to regulate up to about 2V below the input voltage (the 12V output from the boost converter).
V1 will not be able to draw 10W because the single boost converter is supplying the two regulators; it is only rated to supply 10W total. There is 4.8W drawn by V2 (12V*0.4A, note that this is 12V because V2 is a linear regulator), thus V1 is limited to 5.2W. edit: However, this limit is above the 4.8W limit of what V1 nominally could draw because of the specifications on the output limits of 12V and 0.4A. So even if V2 was not present, V1 could never deliver 10W.