You are doing well Dean
I was born in Scotland but spent many formative years in South Wales there I developed a defensive strategy of learning how to pronounce Welsh place names and modified my diction to make myself understood. I remember well at any early age learning how to say birrd instead of burrd to get peace from the incessant demands of my kindly schoolfriends. I remember Wales and the Welsh with affection as I found them good people. In all our time in Wales I don't think we ever met another Caldwell.
On returning to Scotland on holidays I found that I almost needed a translator as I had no knowledge of what my grandfather was talking about when he was referring to the "lum" or what "drooket" meant.
It is obvious that people grow away from the national idiom. My father could "sort of" understand Burn's poetry but I have to have most of it translated. My chldren would not have a clue.
I sound Scots to the non-Scots but the real Scots can't understand me either.
Yep - Caldwell's came from many places to the USA, Canada, Australia and New Zealand and wherever else but most of them seem to have come from the original homelands as you would expect. At a rough guess the proportion of immigrants to Australia bearing the Caldwell name has been:
4 Northern Ireland : 2 Scotland : 1 England. Some of those nominally from England might have been Scots families.
As for as the origin of the name is concerned the favourite still is caelde weille old English cold water. I don't like that theory for the Scots family but the weight of opinion still favours it.

The more that I think of it,he more alternatives I find, I like to put them up to see if anyone agrees with me and can supply further evidence to back it.

In the midlands of England Caldwell seems synonimous to Chadwell to the extent that the names are almost interchageable. There is a Caldwell Hall at a village of Chadwell.

Chadwell is easy to categorise as it comes from the Mercian Bishop and Saint "St Chad" or "St Caed" he was Bishop at Litchfield Cathedral and had his own holy well which was venerated to this day (it has been rehabilitated). Litchfield Cathedral is unique in the UK as having three equal sized spires. If you turn them upside down they look awfully like the "piles" on the Caldwell Coat of Arms and the waves on the lower part of the shield could well represent the waters of the well.
Reaney in his "Dictionery of Surnames" categorised Chadwell as a version of Caldwell.
This theory would have Chadwell/Caldwell's coming to Scotland in the train of FitzAllan or de Morville. Their lands in Shropshire were not too far from Litchfield and certainly close enough for a pilgrimage. The Chadwell/Caldwell's were proably named as persons who had been on a pilgramage to St Chad's Well.
Wells were and are still venerated in the Midlands of England - a practice which probably pre-dates Christianity and is probably a relict of the worship of Teutones.
In one swoop I have put up a possible source for the name, the family's origins, the meaning of the coat of arms, and our affection for wells.
The trouble is that there are many possibilities and they all are plausible to a degree.

(I have a photograph of Litchfield Cathedral and those spires have such a resemblance to the piles on the coat of arms that it almost made my flesh creep when I first saw it)