Hi Andrew, I think what you are saying is the simplest and easiest, and therefore probably the most correct, way of looking at this question of the relationship between Bride and the Cailleach.  I think our problem today is that we have lost the 'mindset', the broad context in which we are to view the ancient stories as they have come down to us, and that causes us to *interpret* them into what we are trying to make sense of as modern people (with two thousand years of Judeo-Roman mindset as a burden that we must offload before we can start to see our ancestor's worldview more clearly).  
As far as I am aware you are correct to say that Bride and the Cailleach are always viewed as two separate entities - even and particularly in Scotland, where their placenames and dedications are distinctly separate in place type and kind.  There is only one tiny reference to the two being linked into one, which is a late tale which says that the Cailleach goes to a well and bathes in it and is rejuvenated into Bride - but, this does come from a Viking-rich area, and I believe that there is a wonderful essay which debunks this tale very neatly, its around on the internet - and sorry I can't lay my hands on it, but I'm sure someone here will know the wonderful essay I am referring to, it was written by a young woman who soon after died. 

The figure of the Cailleach, with her sacred mountain and wild mountain animals such as goats and stags, is not hard to find all over the western world.  She is often referred to today simply as the Great Goddess, she is the deity of the earth, as represented by the sacred mountain, and the mother of all living creatures including mankind.  In Scotland, her name occurs on many spectacular mountains, usually those with the classical 'volcano' form of the trianglar cone.  And as the deity of the earth/mountain, she also creates/controls the weather, as we can see any day in Scotland - or Greece or wherever - we just have to stand and watch the top of the mountain to see it veiled in the clouds and winds to create the rain and storms.  As the mountain, she also has a cloak of white snow around her shoulders, which we see in the tale where she shakes or washes it to make the snow storm.  But does this make her a goddess of winter?  I'm not sure that it
  does, it  makes her the goddess of weather that's all, as we see in other countries.  Its just that in Scotland, the high Cailleach mountains are so often the source of freezing weather and snow so that it tends to *look* that way.  But all we have to do is go a little south even, and we find that her name turns into the Scots Carlin, and she loses a fair bit of her cold sense (although she does remain 'blue' poor dear :-).    

Brigid is not associated with the sacred mountain, she is primarily associated with the primal element of fire, the warmth of the hearth, healing, the smithy, and, she is covered with stories and symbolism of the biggest manifestation of fire in the world - the sun.  Not for nothing does Patrick call the pagan Irish sun-worshippers, then follows up with Brigid, the Sun of the Irish!  and considering that his new religion is busy moving all sun symbolism to the new male figure of Christ, that is one culturally mixed up saint! But he wasnt just using some sort of kenning, he lived in a pagan world, and would have known and understood precisely the import of what he was saying. Brigid's stories are full of references to the sun, and to the symbolic spiral of the sun, and she is the young sexually-potent fertile 'bride' whose mating with Angus brings spring back into the world at Imbolc.  (And how ironic is it that St Brigid becomes a type of vestral 
 'virgin' ... but even then, if we look  at the vestral virgins of Rome with their sacred fire, its clear that these women are symbolic - not of sexual repression, or of a lack of sexual tension - but of the huge explosive sexual potency and fertility of the young woman, full of fire ...) 

So, back to the primary question - how are we to look at the relationship of Bride to the Cailleach?  We know the story of how Bride is 'held' by the Cailleach, and found by Angus, and their consorting brings spring (warmth and fertility) back into the world.  And this close relationship between Bride and the Cailleach lies at the core of out problem of perception here.  But, this tale of the 'sun goddess' is a truly ancient one, and the experience of the sun setting each night, and of spring returning with the sunnier days each year, is one common to all Europeans.  And if we look at *all* these tales, we find something very interesting in a lot of them.  Each night, the young goddess of the sun is said to be greeted, bathed, and 'put to bed' by her mother, the earth.  In other words, the young daughter, the sun, Bride, sinks into her mother, the Earth, the Cailleach.  And its only a minor extension of that idea to understand that in winter 
 months, her mother keeps her in the earth with her for longer and longer each night, thus depriving the world of her daughter's warming fire.     

And so, we start with a story that describes the young daughter, the Sun goddess, Bride, who rests each night in her mother, the Earth goddess, the Cailleach.  Two different, but closely related, primal deities.  But the effect of her mother (note, not an infertile 'hag') keeping her daughter longer with her each night in winter, results in less daylight, less fire, less warmth, during winter.  And so, superficially, it seems that the story is about a winter hag versus a summer maiden.  But that's 'our' problem... 

PS.  Just as I was about to hit the send button, Andrew your next post just came through and I see you are basically saying much the same thing about the nature of both Bride and the Cailleach - and of course you end with another mother-daughter pair in Demeter and Persephone - which is yet one more example of this same pair I would suspect, but the critical thing as you point out to Bernard, is that you can't take just one set of mythology and draw exactly parallel lines to another, you can only take the general 'concept' of a primitive tale, as each telling of the same basic tale will have its own flavour and variations - in the case of Demeter, she is the goddess above ground who weeps for her daughter while she is in the underworld, a small variation but similar enough in nature and purpose to suspect the same origin myth.