Well, I've been doing that job (flowing translations into InDesign templates) since InDesign CS came out. There are quite a few ways to do it. Eugene's suggestion is a good one, but I have only set up a few translation workflows with InCopy. Translators usually find it quite limiting - it's not meant for a multilingual workflow, and sometimes you absolutely need to tweak settings that InCopy users can't adjust, in order to make a correct translation.
Most translation memory tools these days can work with IDML exported from InDesign. You can ask your translation provider which tools they use, and find out if they support translations in IDML. I've had good luck with firms using memoQ.
There are some other tools that allow this, but they almost all have some limitations in some use cases. If you can tell me your source and target languages, and maybe post a sample of your brochures, I might be able to suggest a third-party tool to you.
The reason that the text doesn't fit the layout anymore after translation is called "text expansion," and you can reduce your text expansion headache by preparing your source language designs for some text expansion before starting the translation process. Well-designed styles and layouts with sufficient usable whitespace will make almost any multilingual layout job easier. You can significantly reduce your amount of post-translation headache by doing these things.
Depending on your source and target languages, you may be introducing significant errors when you flow your provider's translations back into InDesign. Multilingual formatting is not easy, and it's hard to know when your translations are being damaged by your workflow (unless you have QA staff on hand to check the translations, or if your readers/customers start complaining).
Lastly, you may want to consider choosing a new translation provider, one with the tools necessary to do the job. Or you can send your current provider to me, and I can send them my resume and tell 'em to subcontract their multilingual InDesign production work to me.