It is quite easy to understand what is a dhatu with this sketch and these definitions & notes. And particularly what a dhammadhatu is (as in SN 14.1/7-10 & SN 41.2).
Dhātus might be considered as graspable constituted elements making up a particular phenomena (e.g. an external ayatana, or even a whole world) - or just a primordial element (e.g. water).
They are grounded manifestations of some kind.
“Grounded”, in the philosophical meaning of being somewhat actualized; as the external sensory fields/grounds (ayatanani) are actualized through the fields of sensory experience.
Dhatus also belong to the later non-sensory worlds (loka).
For instance, (on the provided sketch,) dhammadhatu is the result (actualisation) of the mental manifestation of the immaterial khandhas, in the namarupa nidana (the nama part). The grounded dhatu is the dhamma as external field of sensory experience (bahira ayatana) -a mental phenomena.
Note that in the last note provided above, a dhathu is usually preceded by some kind of desire. There is usually a desire attached to it. Which might not be the case for a dhamma.
A dhatu might just be a desirably graspable dhamma. While a dhamma is just being a causally conditioned phenomena, originating from the khandhas.
“He (the Sambuddha) then taught me the Dhamma:
Aggregates, field of sensory experience, and elements”.
So me dhammamadesesi,
khandhāyatanadhātuyo
SN 8.12
And please Coëmgenu, you are a very smart young lad. Why are you trying to make Mahayana the prominent school.
What we are trying here is to find the common denominator of all early schools.
A non-schismatic original Buddhism.
Remember that the Loooooord said “no schism!” 
