Adding two lights to existing light
The proposed wiring shown as Revision 1 in the original drawings is not code compliant. Under NEC 300.3(B), all wires for a given circuit must be in the same cable or raceway. In your example, the new lights get the hot lead from a single wire from the switch and the neutral from a separate cable or raceway from the old fixture.

Basically you need a balanced load in each cable or raceway (hot out/neutral back or hot out/switched hot back) to prevent the possibility of induction heating.

As @Speedy Petey suggests, a much simpler, and code compliant method, is to run a cable with a neutral and a switched hot from the existing fixture to the new fixtures.

UPDATE: Based on the added drawing in Revision 2, the proposed circuit is now code compliant. Also, as @Ben noted, any white wire used as a hot that is exposed in a box or fixture must be marked black or red with tape, paint or marker to show that it is hot.