'And one in a velvet gown' and 'And some in velvet gowns' are both found in print sources. 'Bags' seems to be a late C19 corruption of the more usual 'tags' (cf 'rags and tags', 'rag, tag and bobtail' etc). Iona and Peter Opie (Oxford Dictionary of Nursery Rhymes, number 140) print 'jags' in their 'standard' text, but it isn't clear that this is necessarily the earlier form; in any case the frequently repeated statement that the rhyme has 'Tudor' origins is mere speculation unsupported by actual evidence. The Opies refer to the suggestion without endorsing it. The rhyme itself first appears in print (Gammer Gurton's Garland) in 1784, but may have been modelled on something earlier; verses in the same metre and with the same opening line (they are otherwise unrelated) appear, for example, in the Westminster Drollery of 1672.

The document Q links to is a particularly pernicious thing, repeating all manner of baseless speculation as 'fact'. Much of it seems to derive (though probably at many removes) from publications such as Katherine Elwes Thomas, The Real Personages of Mother Goose (Boston, 1930) in which bizarre theories from the fevered imaginations of some very eccentric people are presented as established fact. The study of folk literature in general is bedevilled with such things, but the nursery rhyme in particular has ever been a playground for those who the Opies (who should always be consulted on such matters; ODNR is still the standard work) tactfully refer to as 'the happy guessers'.

Carmel's family rhyme does seem to be a collation as 'Snuffy' suggests, with some further alterations made (the church/shirts part I haven't located; perhaps it is peculiar to this example?). What part of the world is your family from? How long have they sung those words?