Could the British press handle HRH Prince Henry be apart of a new realm and family.Since he was the second born son of Charles and Diana ?

What do you mean? Harry can not be made King of a new realm by the press. According to laws set down by Parliament, there is one monarch for the realms of the United Kingdom and Commonwealth Realms. The press does not write laws.

Not going to happen, so they would have no problem with it.

All shall bow to the new king and queen, Their Majesties King Charles and Queen Camilla.