[HUE]

That's a good question. But I always hesitate answering these kinds of questions, because I'm far from a grammar genius. There are also so many different "authorities," and some give conflicting information. In a lesson, I would probably correct the sentence to "If we worked harder, we wouldn't have so many problems." This would be in preference to any long grammar explanation that is mostly applicable to this one example. If a student really, really needed to know the grammar particulars, I would spend a few minutes after the lesson.

That said...

For some reason, the problem sentence just doesn't sit well with me. I'm not really sure why, though.

We can use "were going to" and "would" in the same sentence, as it suggests an imaginary situation in the future. For example: If we were going to work harder, I would expect a raise. This means that we aren't going to work harder, and I don't expect a raise. We can also change the sentence slightly to make a suggestion (which often uses a be-verb), as in: If we were going to work harder, I would expect a much larger bonus!

I think the sentence sounds a little off because it's so much simpler to say: If we worked harder, we wouldn't have so many problems. Including "were going to" doesn't add any special emphasis.

But I'm going to throw this one out to the forum, and see if there are any grammarians dieing to answer it.