Which 1936 act makes it illegal to recruit and/or transport individuals across state lines for the purpose of interfering forcefully or threateningly with peaceful picketing or the right to self-organization?

The movement or recruiting of people across state lines to interfere with picketing or organization was explicitly banned in 1936 by the passage of the Byrnes Act. This is also known as the "anti strikebreaking" act, appropriately, and makes the conduct of any such behavior a felony.

I believe the answer is Byrnes Act (1936)

The purpose of the creation of the Byrnes Act is to prevent labor union from conducting strikes.

Through this law, the police department had enough ground to throw the people who came from other states to support other members of labor union in doing collective bargaining to the jaail.