What is the linguistic term for an environment where parents teach a second language to their children in lieu of the parents' native language?

To my knowledge, there is no single term that describes this situation. It is merely one of the many configurations that arise in multilingual environments.

Also, there is not just one single way in which this arises. The examples could be.

1. Parents do not speak each others first languages and communicate using a third language.
2. One of the parents speaks a language of the other parent who does not speak the language of the first parent. The children are only exposed to the language of the other parent.
3. Parents only speak a third language to their children to speed up their integration and/or promote their linguistic skills in another language.

All of the above can happen in all sorts of combinations of linguistic environments. For example, the neither of the parents speak the dominant language of the country they live in or one of the parents speaks the local language.

There are also various scenarios of prestige and power that will influence how this will play out.

So it seems that one term would simply not be able to describe this phenomenon accurate but it is possible that a term is used somewhere in the very specialist literature on bilingualism.

Another place to look would be research on language contact and especially creolization which often arises in contexts where children acquiring a third language is common in a linguistic area.