Let me stop you there. Spiritualism is belief in and making contact with human and angelic spirits. In it's broadest sense spirituality encompasses those aspects of human life not susceptible to material investigation.
That's two different entirely different definitions in one paragraph, neither of which has any demonstrable basis.
In my days as a school governor we were charged via the national curriculum to educate and develop the spiritual aspects of our charges and that was in all schools.
The National Curriculum, though, and the Education Act 2002 (and the subsequent Academies Act 2010) fail to provide any definition of 'spirit'. Ofsted's doesn't provide a definition, but does explain what it looks for in this area:
ability to be reflective about their own beliefs (religious or otherwise) and perspective on life
knowledge of, and respect for, different people’s faiths, feelings and values
sense of enjoyment and fascination in learning about themselves, others and the world around them
use of imagination and creativity in their learning
willingness to reflect on their experiences
That doesn't sound anything like the definitions you put up, so that's a third. (I do take issue, slightly, with 'respect for different people's faiths' - their right to them, perhaps, but not the faiths themselves).
In other words non religious spirituality.
The problem isn't with divorcing religion from spirituality, or with trying to see religion as some sort of 'subset' of spirituality, but rather with giving any sort of meaning to 'spiritual'.
You do not consider these to be spiritualism(sic) because you have a narrow interpretation of spirituality which conflated spirituality with religion.
No, I have a problem with 'spiritual', because it's intrinsically linked to a notion of 'spirits' which don't appear to be real.
O.