The way you have written your first set of sentences, you must use the verb "to get," otherwise the sentence does not make sense - I must get my homework done.
But you can express the same idea, more simply, by saying "I must do my homework before the film starts."
Or, you could say "I have to do my homework before the film starts."
Note: you have to use "to," after the verb 'have,' in the present tense but you must not use it after the verb "must." The verb "must," takes what we call the zero infinitive in English. The full infinitive of a verb includes the word "to," "to have," "to play," or "to make," for example. Some verbs, such as "must," "would," and "could," are followed directly by the verb itself without the word 'to,' in front of it. This is the zero infinitive. So, we have:
I have to score more goals.
I want to score more goals.
I could score more goals.
I must score more goals
I should score more goals.
I shall score more goals.
I will score more goals.
Your second sentence should not use the gerund. You would say:
"The teacher forced the students to work together."
The construction involves the simple past tense (forced or made) and the object of the sentence (the students) is then followed by the full infinitive ("to work")