Attempts to rigorously define "word" as distinct from other word-like combinations of morphemes have not been successful in the field. So the short answer is, there's no way to tell; the slightly longer answer is that it depends on your criteria for calling something a word. Or, since you ask about word forms, what is the difference between "two words" and "two word forms"? And more to the point, how would you validate a given definition of "word" or "word form"?
Your underlying interest seems to be about the contribution of phonological differences in defining "same word (form)". The conventional view is that "a word" is some combination of morphemes, which serves as the input to the phonology. Rules of the phonology act on that input, and you get a pronunciation. If all phonological rules were obligatory, there would be only one pronunciation of a given input: but not all phonological rules are obligatory, which means that there can be two or more pronunciations of some words. For example "winter" can be pronounced as [wɪ̃ntɹ̩] or as [wɪ̃ɾɹ̩], but both come from the same input, /wɪnt(V)r/ and differ in whether deletion of n happens (the rest is automatic). By that definition, the two pronunciations would not be different words. "Winter" and "winters" would be, though, because the latter has an inflectional morpheme lacking in the former.
It is not clear whether the "-in'" affix is a distinct morpheme from the "-ing" affix. Perhaps there is one affix /ɪŋ/ which optionally changes to [(ə)n], or perhaps there are two underlying affixes, /ɪŋ/ and /ən/. The questions that we would ask are, are the two affixes distributed identically or does one appear in a position where the other cannot (and does that matter)? and, does it matter that there are no general phonological rules of English that turn /ɪŋ/ into [(ə)n] or vice versa. As a phonologist, I tend to favor making such differences be part of the input to the phonology (not complicating the phonology with arbitrary rules), and I imagine syntacticians favor dumping the problem into the phonology and keeping the syntax clean. This is why a "readjustment component" has been posited. There is no clear answer to the question about the analysis of -ing vs. -in', in terms of 'one thing or two'.
As for two pronunciations of "daughter", I don't know why there would even be two pronunciations of the word. Let's take the word [kɔt], which can also be pronounced [kat]. For some people, [kɔt] is the past tense of "catch" and [kat] is a thing you sleep on; for others, these are slightly different ways of pronouncing the words caught and cot. "Caught" and "cot" are generally considered to be different words, and for some people they are actually pronounced the same. I'm one of the "pronounced the same" speakers, but I know that my vowel is somewhat different from the vowel used by some (younger) speakers in Central Ohio who use a backer vowel but still pronounce the two words the same. So turning to "daughter", my pronunciation of the word would be different from that of those speakers. Does that mean that there are different inputs to the phonology?
Well, yes, in fact I pronounce the word "daughter" the same way as my brother, and those are different words because my /datr/ is in my grammar, and my brother's /datr/ is in his grammar. As you can tell, I'm reflecting the viewpoint that a grammar is a fact of individual psychology and not a social object. If you consider concepts of "word" from a social viewpoint, where we are attempting to characterize all forms of English, then you could come to the conclusion that two dialectal pronunciations of "daughter" are different phonological outcomes for the same word.
So it depends on how you define "same word" and "same morpheme".
