DH Re-entry

[JL87]

The DH is used in the 4th slot of the batting order for the right fielder. The DH is slow, but has a great stick. The right fielder is fast and has a great glove, but can't hit the ball. The DH is Player A and the right fielder is Player B.

In the 1st inning, the 4th slot of the batting order comes up and Player A hits a single and gets on base. The coach puts in Player B for Player A and this terminates the DH for the rest of the game. After the half inning, Player B goes on the defense for the next two innings. In the 4 inning, the 4th slot of the batting order comes up to bat and the coach puts in Player A for Player B. Player A uses his re-entry. Player A reaches first with a single and the coach puts in Player B using his re-entry. This terminates Player A for the rest of the game.

Did Player B use two re-entries?
When Player B replaced Player A in the 1st inning, did he
use the re-entry or the substitute rule?
Since Player A and Player B are both in the same lot of
the batting order, Player B just replaces Player A
and is still legal?
What is the correct ruling?