Thank you, I had bookmarked this comment to reply to with exactly this. Her name was Martha/Marta, yes, and she was a Lithuanian peasant, hence the scandal, and I was going to say that if he hadn't loved her very much, she wouldn't have been tsarina! Peter had her crowned during his lifetime, and then she succeeded him after his death as Catherine I (hence why Catherine the Great was Catherine II) and ruled until her own death just two years later.
Re: Prussian/Danish Relations according to Stephan Hartmann: The FW Era (and some spoilers for Frit
read Massie, Cahn :P