She was supposed to/had to/was to fly to Brussels

Solution 1:

The presenting example sentences

1. She said she was supposed to fly to Brussels, and didn't know when she'd return.
2. She said she had to fly to Brussels, and didn't know when she'd return.
3. She said she was to fly to Brussels, and didn't know when she'd return.

are all grammatical and all suitable for the same occasion, though they don't mean the same thing -- (2), for instance, means she was under an obligation to go, whereas (1) and (3) are only expectations.

But all indicate an expectation of imminent travel, without information about return. We get this plethora of constructions in English because it lacks a future tense -- will is just another modal auxiliary, and so is must, which is had to in the past, and any modal can refer to the future. So can their periphrastic equivalents -- must = have to, will = be going to, should = ought to, can = be able to, etc.

We don't really need a future tense in English; after all, the present and the past can refer to any time at all already.

As for using the progressive/continuous construction, that's OK, too

4. She said she was flying to Brussels, and didn't know when she'd return.

and means the same. The progressive is often used to indicate things that are in the near future -- I'm leaving today.

And, while was supposed to can introduce an event mishap, it doesn't need to.
If that's all she could say, that's all she could say.