doesn't have to / won't have to

[Verona_82]

Hello,

Both the sentences are correct, but which sounds better?

She doesn't have to get up early tomorrow.
She won't have to get up early tomorrow.

To what extent does the present form cover the future?

Thank you.

[billmcd]

Hello,

Both the sentences are correct, but which sounds better?

She doesn't have to get up early tomorrow.
She won't have to get up early tomorrow.

To what extent does the present form cover the future?

Thank you.

"Extent"? Either form is correct.

[Verona_82]

Thank you for the reply.
I should have explained what I meant better.

Would you prefer
"I have to go on a business trip next month (year?)"
or
"I will have to go on a business trip next month (year)" ?

[bhaisahab]

Thank you for the reply.
I should have explained what I meant better.

Would you prefer
"I have to go on a business trip next month (year?)"
or
"I will have to go on a business trip next month (year)" ?

Use the first one.

[Verona_82]

Could you please explain why?

[bhaisahab]

Could you please explain why?

For me the second one implies some sort of condition, the first one doesn't.

[Verona_82]

Thank you! Would you mind answering one more question, please?

Would you correct the answer if the task was to express lack of obligation and your student wrote "I won't have to ...(do something).... tomorrow/next week/in autumn" ?

[Raymott]

Thank you! Would you mind answering one more question, please?

Would you correct the answer if the task was to express lack of obligation and your student wrote "I won't have to ...(do something).... tomorrow/next week/in autumn" ?

Here's my take; it's similar to bhai's idea that there's something conditional about "I won't have to ..." or "I will have to". I'll illustrate with the positive phrase, but it applies to both.
"I have to ..." suggests that the state of things as they are mandates that I do something. Nothing else is necessary.
"I will have to ..." suggests that perhaps something else must happen to complete my obligation. Although it is fully expected to happen, it might not; and that could change my obligation.

I'm thinking of an event that is expected to occur between saying "I'll have to ..." and the time that I'll have to do it. Stated conditionally, an example would be "If more students turn up tomorrow, I'll have to work harder than usual." Now, let's say that you have a list of students who have signed up, and the number is greater than usual. So you fully expect that you will have to work harder tomorrow. You could then say, "I'll have to work harder tomorrow."
If you said, "I have to work harder tomorrow", you could be wrong, since there is a possibility that all those extra students won't show up. So there is something tentative about "I will have to ..." and it's a weaker statement than "I have to ..."

To your question: It's not just a matter of expressing obligation. If your boss has told you today that you have to work harder tomorrow, and you can see no way of avoiding it, you should say, "I have to work harder tomorrow."
However, if there's a condition ("I'll have to work harder tomorrow if I want to get this finished by the weekend") or an expectation that might not be fulfilled ("I'll have to work harder tomorrow because Suzy was sick today and probably won't come in tomorrow), then you use "will".
If there is no such condition or expectation, I'd probably correct that answer, but not deduct marks or mark it wrong.

[Verona_82]

Thank you for the insight, Raymott. It's very helpful.