[williebfree]

R 6-3-5 . . . The opportunity to make an alternating-possession throw-in is lost if the throw-in team violates. If either team fouls during an alternating-possession throw-in, it does not cause the throw-in team to lose the possesion arrow.
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In response to the original situation, call the kicking violation on the first (And only AP throw-in attempt).

By rule, R 4-41-5, the AP throw-in ends when AN inbounds player (other than the thrower) touches it.

Therefore, the AP switches AFTER THE FIRST throw-in attempt was completed, when kicked by B1.

Now, administer the second throw-in (as the result of the kicking violation).

What has happened? Team A has ultimately been allowed to make the throw-in which it was entitled to AND Team B now has the arrow.

Can it be any more simple (or dificult) than this?