Difference between "must have worked" and "must have had to work"
Could you please help me with understanding the difference between these two constructions? Is there any difference in meaning ? In what cases I should use the last option (must have had to do)?
Here are examples:
1) Without things like washing machines and dishwashers our grandparents must have worked/ must have had to work much harder in the kitchen than we today.
2) I wonder how you get permission to go into the building. I suppose you must have shown /must have to show some form of identification.

Question

Difference between "must have worked" and "must have had to work"
Could you please help me with understanding the difference between these two constructions? Is there  any difference in meaning ? In what cases I should use the last option (must have had to do)?
Here are  examples:
1) Without things like washing  machines and dishwashers our grandparents       must have worked/ must have had to work    much harder in the kitchen than we today.
2) I wonder how you get  permission  to go into the building. I suppose  you     must have shown /must have to show      some form of identification.

Answer

1) Our grandparents must have worked much harder in the kitchen than we do today. 
 =  I assume they worked harder

Our grandparents must have had to work much harder in the kitchen than we do today.  
= I assume they needed to work harder

The difference is that the inclusion of 'had to' suggests necessity or obligation. It's the same as the difference between 'I work hard' and 'I have to work hard'.

2) If this is an example of the same construction, the sentences should read like this:

I suppose you must have shown some form of identification. 
= I assume you showed some ID

I suppose you must have had to show some form of identification. 
= I assume you needed to show some ID.