This is not forgery in the usual common law country sense of the word (the statute linked has a definition broader than the usual legal meaning of the term, and I don't have an opinion on what is fraud in a will under that statute). I've never seen the word "forgery" used in the sense of the question in any U.S. case or statute.
The first example (gun to head) is a will invalid as a result of duress (very unusual for a will, although the related notion of undue influence which is generally much softer is the most common ground for a will contest, something I've probably litigated a dozen times). The following is from a brief that I wrote in an undue influence will contest where I successfully defeated a will contest based upon undue influence allegations:
Undue influence means words or conduct, or both, which, at the time of
making a will (1) deprived the person making the will of his free
choice; and (2) caused the person making the will to make it or part
of it differently that he otherwise would have. Scott v. Leonard, 117
Colo. 54, 184 P.2d 138 (1947); Snodgrass v. Smith, 42 Colo. 60, 94 P.
312 (1908); In re Shell's Estate, 28 Colo. 167, 63 P. 413 (1900).
An adult of sound mind who is not acting under undue influence may
devise his property to whomever he or she desires; the fact that a
will may contain provisions that differ from the trier of fact's idea
of what would be proper is not enough to invalidate the will for undue
influence. Aquilini v. Chamblin, 94 Colo. 367; 30 P.2d 325 (1934);
David v. Davis, 64 Colo. 62, 170 P. 208 (1917); Lehman v. Lindenmeyer,
48 Colo. 305, 109 P. 956 (1909); In re Shell's Estate, 28 Colo. 167,
63 P. 413 (1900).
Influence gained by reason of love, affection, or kindness, or by
appeals to such feelings, is not undue influence. In re Rentfro's
Estate, 102 Colo. 400, 79 P.2d 1042 (1938); Aquilini v. Chamblin, 94
Colo. 367; 30 P.2d 325 (1934); Blackman v. Edsall, 17 Colo. App. 429,
68 P. 790 (1902).
One should not draw an inference, however, that a person exercised
undue influence over another person solely because they were in a
confidential and/or fiduciary relationship. Krueger v. Ary, 205 P.3d
1150 (Colo. 2009); In re Estate of Romero, 126 P.3d 228 (Colo. App.
2005); In re Estate of Schlagel, 89 P.3d 419 (Colo. App. 2003).
Similarly, undue influence cannot be inferred solely because one or
more persons may have had a motive or an opportunity to influence the
testator in the making of his will. Scott v. Leonard, 117 Colo. 54,
184 P.2d 138 (1947); Snodgrass v. Smith, 42 Colo. 60, 94 P. 312
(1908); In re Shell's Estate, 28 Colo. 167, 63 P. 413 (1900).
The fact that a person was in a confidential and/or fiduciary
relationship with the testator, benefited from the Will, and was
actively involved with the preparation or signing of the will, is a
set of facts from which a trier of fact may drawn any reasonable
inference, but this does not create a presumption of undue influence
when it is rebutted, for example, by evidence tending to show that any
influence was gains from an appeal to love, affection, or kindness.
Krueger v. Ary, 205 P.3d 1150 (Colo. 2009).
The second example is called fraud in the factum and is quite rare but has been litigated and is discussed in detail in this 1920 law review article. In twenty-five years, I've litigated two fraud in the factum cases, one involving the substitution of language in a long contract at the closing table in a complex business deal and the other involving a deed in a quiet title dispute involving a long and messing chain of title with wild deeds, etc., but none involved a will.
I am aware of one will case involving a genuinely forged will, where a client of the first law firm where I worked brought in a woman whom he represented to be his wife to sign his wife's will and deeds from the wife (who was actually an imposter), that took place shortly before I joined that firm as an associate attorney. The notary and witnesses to the will signing were later called in after the death of the wife in a will contest as trial witnesses to describe the woman who signed the documents which established the forgery since she looked nothing like the actual wife (different hair color, different height and build, twenty years younger, different handwriting, etc.). Spoiler alert: The husband didn't win that case.
The 1920 article also addresses the vanishingly rare case of a will procured not by duress or undue influence, and not by fraud in the factum, but instead by fraud in the inducement (e.g. telling someone who is about to write a will that they did something highly disrespectful to a parent causing the parent to write that person out of their will when in fact the account was a total fabrication).
There is a specific doctrine that provides that the federal courts do not have jurisdiction over probate cases, recently reaffirmed by the U.S. Supreme Court in a case involving Anna Nicole Smith, so it is unlikely that there is much relevant and authoritative case law in the will context in federal court.