According to my understanding

1. He was to come at 8 pm.  

(Means He was supposed to come at 8 pm)
2. He had to come at 8 pm.  

(Means He was obligated to come at 8 pm)

And also 

1. How she would feel if her mother was to be made to stand and wait  

(Means her mother was asked to stand and wait by someone)
2. How she would feel if her mother had to be made to stand and wait  

(Means her mother had to stand and wait till a chair was free)

Correct me if I am wrong.