Delaware corporation claims "internal affairs" doctrine prevents me from piercing corporate veil or alleging alter ego in a claim against a nursing home chain hiding behind its shell corps and Delaware law in order to defeat my recovery.

Answer: I think your opponent misperceives the function of the internal affairs doctrine. It does not apply to your case but rather applies only to questions about disputes or the relationship between and among the corporation and its directors and shareholders. The Supreme Court of Delaware probably best explains this disctinction in McDermott Inc. v. Lewis, 531 A.2d 206, 214-15 (1987).