"I should have been" and "I should have to be" I saw these two phrases in a book. Is there any significant difference of meaning?
Yes there is:
If you had been invited to Buckingham Palace for a reception and drunk a little too much, you might reflect afterwards that: "I should have been on my best behaviour".
On the other hand, if you were to receive such an invitation, you might reflect beforehand that: "I should have to be on my best behaviour".
That's to say: The first example refers to your (mis)behaviour in the past and the second reflects on how you should behave in the future.