'If your mother knows, we are in trouble.' might be a 'first conditional' construct in one possible sense of that sentence, because it is possible in English (as well as in many other languages) to use a present tense construction to represent the future tense. (Also there is the 'present continuous' or 'present progressive' tense, e.g. 'We're doing the Macarena in our dance class next week.' which is similarly a future construction despite the apparent present tense.)
So, you could also say 'If your mother knows, we will be in trouble.' or 'If your mother knows, we are going to be in trouble.' each of which could mean the same thing, if, for instance, being in trouble is taken in a way that requires you already have had consequences laid down.
However, I am not sure I would put it in the first category outright, since there is at least one more way to read it: 'If your mother knows, we are in trouble (right now).', in a case, for instance, where being in trouble is taken as meaning that the person with whom you are in trouble has already decided that you are in trouble, but without requiring that you have already found out about it.
I generally take 'X is in trouble with Y' to mean that 'Y' has decided that 'X' is in trouble, and as independent of whether 'X' actually even knows that 'Y' has decided such. I don't think of it as having any requirement that the person in trouble actually has been notified. As mentioned elsewhere, this would seem to be a case that falls somewhere outside the typical 'formula' for a 'first conditional'.
However, given that your question was how the sentence was a first conditional, I would imagine that the sentence was regarded by the person who presented it as such as having a meaning such as in the first case (= 'we will be in trouble') rather than the second, and thus it would fall into the first category due to that equivalence.