The Household religion

I'm still skeptical about that idea though. There is much of Minoan religiosity that we don't know, and Mycenaean religion is perhaps better known, but also only very fragmentary. But admittedly I never read the works you cited, so i'm not a fit judge.

J_Agathokles is right — though actually, it is probably better said that we do not actually know anything at all about Minoan religion. We don't have any evidence supporting any identity of the 'woman with snakes' statue that was found at a Minoan-era site. It might be a goddess, it might very well not be a goddess. However, being as the image is clad virtually identically to the paintings we see of Minoan women, and the fact that we do not otherwise have any evidence of images of Minoan divinities, the 'snake goddess' likely represents a human engaged in some action involving the carrying of snakes. What this means, we don't know. It may be symbolic, or it may represent a literal practice of the Minoans. 

Pemphredo wrote:that one of the most popular goddesses could be part of the household worship

Any god can form part of household worship . Although there are particular powers associated with the maintenance and safety of the home, what powers any family worships at the home altar is a matter of that family's situation, circumstances, experiences and discretion. It is unquestionable that Minerva/Athini was a focus of worship in numerous households — votive figurines of her abound from a variety of archaeological sites.

Erodius wrote:...it is probably better said that we do not actually know anything at all about Minoan religion.

Exactly. And since no attributes or actions are unique to certain figures depicted, we can't even tell for sure which figures depict deities, and which depict humans. We simply don't know. There is a Minoan seal ring that I've seen explained as two priestesses worshipping a manifesting Goddess shown three time in the picture to depict different stages of her manifestation, and others explain it as five priestesses performing a ritual dance. Again, we simply don't know.

Honnestly: I always thought that the "snake goddess" wasn't a goddess at all but, like you said, a priestess.

Pemphredo wrote:Honnestly: I always thought that the "snake goddess" wasn't a goddess at all but, like you said, a priestess.

We really cannot even say if the Minoans had anything equivalent to a priesthood. Rather than a 'priestess' it may simply represent a woman performing some sort of dance or, perhaps, a ceremonial action involving picking up the snakes — if they are even snakes. 

The 'goddess cult' theorist disciples and admirers of Marija Gimbutienė are quick to label anything resembling a female figure found in an archaeological site as 'proof' of a vast Mother Goddess cult of a matriarchal ancient world. However, this doesn't make it true. One archaeologist Cathy Gere says that: "Through the example of Knossos on the island of Crete, which had been misrepresented as the paradigm of a pacifist, matriarchal and sexually free society, we can see how archaeology can easily slip into reflecting what people want to see, rather than teaching people about an unfamiliar past."

I'd recommend reading this article by archaeologist Andrew Fleming:
The Myth of the Mother Goddess