There are a bunch of things mixed together in the opening post which make it unclear.
- daughter did level 5 RCM - that's practical and in Canada?
- her piano school teaches all rudiments together at once
- the question of exams from different countries (and different institutions?) being accepted by the RCM
Where do the different countries fit in? Is the school in the US, or a US-based private school located in Canada?
Something seems topsy turvy in the question itself. The RCM is one of a number of organizations that offers exams, but who looks at those exams for what purpose? Well, a university might, if you are applying to study in music. In that case they want to know what you studied, and it doesn't matter where you studied it. So you have the certificate from that school and other certificates from the RCM. You wouldn't need the RCM to write that the school's certificate is an equivalent of theirs.
Otoh, you get certain certificates from the RCM only if you pass both grade 5 and the preliminary theory exam. If you want to know if they will accept the school's exam, in order to get that certificate, why not ask? They have a phone number, and I have found the staff there very open and helpful.
Her piano school offers a theory class teaching both Preparatory Rudiments & Basic Rudiments together or teaching all rudiments together(Preparatory, basic, intermediate & advanced). They don't teach rudiments level by level.
Having both studied, and later taught, the RCM rudiments using the Wharram book, what you are describing bothers me. You don't want to just get a certificate - you want to have solid learning. Here's my thinking on it.
The Rudiments has separate chapters on various concepts, and these concepts interrelate. For example, if you learn what intervals are in one chapter, those intervals come into play in the chapters on scales and chords. There is only so much that the mind can absorb.
At the Preliminary level you very thoroughly learn basic concepts: simple intervals (major, minor, perfect), simple chords (major, minor, recognize Dominant and Tonic), key signatures only up to 4 sharps and flats, since 5-8 double up (F# & Gb major are equivalents, etc.) and it's too early. The various chapters reinforce each other.
At the Intermediate level you use the concepts that you have learned, and you expand and go more deeply. You invert your intervals and add augmented and diminished; ditto with chords. You add your scales that have enharmonic equivalents. You use the chord types you learned and get into the simplest form of cadence and melody writing. You learn to transcribe in octaves.
At the Advanced level you start manipulating the chords to discover things in music. You can work in four clefs: treble, bass, alto, tenor. You can work with major and minor scales, as well as octatonic, whole tone, blues, and you've been introduced to modes. You are transcribing close and open score, transcribing into different keys and clefs (example: closed score in treble and bass clef, written for a string quartet and so using treble, alto, and bass clef).
That is a lot of information. The three exams are spread over a number of years for a reason. I can't see everything taught at the same time working unless it is simplified - in which case the same things are not being taught - or it takes a long time - or it is crammed. You don't want crammed. These are fundamental, basic concepts which should be understood well if going that route.
There are alternative ways of studying music, such as starting with analysis and deriving fundamentals from them. But that's not under discussion here.
