how hard is it to prove alienation of affection in the court of law?

Answer 1

States That Still Recognize Alienation of Affections
Despite criticism that alienation of affections lawsuits are outdated, several states still recognize alienation of affections, having upheld as much as $500,000 in punitive damages for the suing spouse. States that still recognize alienation of affection include:
Illinois
Mississippi
Utah
North Carolina

Answer 2

that your husband or wife is cheating on you (proof, pic, emails, etc) and either is or has left you for this other person.