The constructions in your [1'] ii and iii are ambiguous between being (a) dislocations and (b) exhautive conditionals. This corresponds to an ambiguity about whether whoever her parents are is (a) an NP (a fused relative) or (b) an interrogative clause.
Both ii and iii can be disambiguated by e.g. coordination with an appropriate construction, here shown on the example of ii:
Forcing the left-dislocation reading:
 Her husband and whoever her parents are, they must be worried sick.
Forcing the exhautive conditional reading:
 Whoever her parents are and regardless of where they are, they must be
As we will see below,  involves a coordination of NPs: her husband is an NP and it couldn't be coordinated with an interrogative clause. Thus,  is a left dislocation.
Contrarily, in , regardless of where they are is an interrogative clause and it couldn't be coordinated with an NP. Thus,  involves a coordination of interrogative clauses; thus, it is an exhaustive conditional.
The key question is always whether whoever her parents are is an NP or an interrogative clause.
What is used in  and  is the fact that (CGEL, or CaGEL, as you call it, p. 1326)
In the great majority of cases, coordinates belong to the same syntactic category, but a difference of category is generally tolerated where there is likeness of function.
The cases where the requisite likeness of function obtains are discussed in CGEL Ch. 15, §3.2 (Coordination of unlike categories, pp. 1326-1329). Suffices to say that none of those apply to  and ; this will become obvious below, because certain attempts at coordination will produce unacceptable sentences.
As we've been saying, the key question is whether whoever her parents are is an NP (if it is, it's a fused relative), or whether is is rather an interrogative clause. However, note that the same group of words may function sometimes as one, and sometimes as the other, depending on the context (CGEL, p. 987):
 i They will appoint Jones, whoever we recommend. [open interrogative]
ii They will appoint whoever we recommend. [fused relative]
The underlined [boldfaced] sequence is in [i] an interrogative clause in adjunct function and in [ii] a fused relative construction functioning as object of appoint.16 The free choice -ever compounds do not occur elsewhere in interrogative clauses—the ever in examples like
What ever could have come over her? has a different sense, and is usually written as a separate word (see Ch. 10, §7.13).
16Whomever is possible as a formal alternant of whoever, especially in [57ii].
So, one key observation is that exhaustive conditionals employ clauses. CGEL gives two main syntactical ways to tell if the construction like whoever we recommend is a clause or an NP.
The first way is to see whether stranded prepositions can be fronted (note the mention of exhautive conditionals—which I have boldfaced—in the explanation that follows the example):
 i He always antagonised whoever he worked with.
ii *He always antagonised with whomever he worked.
iii Now, in whatever way government may be theoretically conceived,
it is in practice a matter of the adjustment of a multiplicity of private interests.
In [i] we have a fused relative with a stranded preposition; as shown in [ii] the preposition cannot be placed in front of whoever. In ordinary interrogatives, both orders are possible: I can't recollect who he worked with/with whom he worked. But [ii] is ungrammatical because the preposition has been placed at the beginning of an NP rather than a clause. The difference between [i] and [ii] is thus comparable to that seen between He always antagonised those who he worked with and *He always antagonised with those whom he worked. The ungoverned exhaustive conditional, however, is a clause and thus allows a preposition to be placed in front position along with its complement, as illustrated in the attested example [iii]. This may be compared with the governed counterpart no matter in what way government may be theoretically conceived.
So, let's modify your example slightly by introducing a preposition;
 i a. Whoever she originates from must be worried sick.
b. *From whomever she originates must be worried sick.
ii a. Whoever she originates from, they must be worried sick.
b. From whomever she originates, they must be worried sick.
iii a. Her husband and whomever she originates from, they must be worried sick.
b. *Her husband and from whomever she originates, they must be worried sick.
The fronted version i b. is not acceptable, which is good evidence that what we have there is an NP. However, ii b is acceptable as it stands. There is, however, a way to force an NP reading and make it unacceptable: we just attempt a coordination with another NP. This is done in iii: as expected, the stranded version (a.) is fine; here the whomever she originates from is forced to be read as an NP. The fronted version in (b.), however, can only be a clause, and so an attempt at coordination with an NP makes the sentence unacceptable.
Place in the system of exhaustive conditionals
The second syntax-based way that CGEL suggests for distinguishing between an interrogative clause an fused-relative NP concerns certain regularities that hold for exhaustive conditionals (pp. 988-989):
Exhaustive conditionals are classified, as we have noted, on two cross-cutting dimensions, governed vs ungoverned and closed vs open:
 GOVERNED UNGOVERNED
closed a. They will appoint Jones [regardless b. They will appoint Jones
of whether he's the best can- whether he's the best
didate or not]. candidate or not.
open c. They will appoint Jones [regardless d. They will appoint Jones
of who we recommend]. whoever we recommend.
On one dimension, the relation of [a] to [b] is the same as that of [c] to [d]; and on another the relation of [a] to [c] is the same as that of [b] to [d]. These relationships are most simply described if in other respects the constructions are all alike—i.e. all involve interrogative clauses.
Let's do your [1'] i first,
[1'] i Whoever her parents are must be worried sick.
If this were an example of an exhaustive conditional, it would be of an ungoverned closed type. It would thus have to have two counterparts: a closed-governed, and an open-ungoverned. But already with the governed counterpart we run into trouble:
[1'] i' *Regardless of who her parents are must be worried sick.
The story is different with your
[1'] ii Whoever her parents are, they must be worried sick.
Here it seems we can have a governerned version:
[1'] ii' Regardless of who her parents are, they must be worried sick.
But again, if we coordinate with an NP, we force an NP reading of whoever her parents are, and it becomes impossible to construct a governed counterpart:
 i Her husband and whoever her parents are, they must be worried sick.
ii *Her husband and regardless of who her parents are, they must be worried sick.
[1'] ii Whoever her parents are, they must be worried sick.
is ambiguous between being a left dislocation (where whoever her parents are is an NP) and being an exhaustive conditional (where whoever her parents are is an interrogative clause). The ambiguity may be lifted by approriate coordination as in  and , as explained above. Only the case [1'] ii is treated explicitly; the right-dislocation case iii is treated the same way, with the same conclusions.
R. Huddleston and G. K. Pullum, The Cambridge Grammar of the English Language (Cambridge University Press, Cambridge, UK, 2002).