We got the same letter for my husbands 3 kids as we didn't do their medicals either. Both his ex wives have full custody as stated on the divorce decrees we submitted. We wrote a declaration stating that he is fully aware that he will never be able to sponsor his kids as family class to Canada. That he fully understood the consequences and could they please be exempt from the application. We explained that he wasn't in his sons lives and that they didn't really know him and if anything happened to their mom, they would be better off with their stepdad and her family. His daughter, we said we spoke to her mom and she refused and left it at that. We also explained that she would be spending her summers with us as per the visitation set by the courts. Three days after they received it, his medical went to passed, bgc started and complete a couple days after that then he got his ppr. It was a 4 month start to finish. A lot also depends on your case officer and we got lucky as I read a lot that they actually had to go to court to get medicals done.
Your ex obviously doesn't want to be found. You should explain it all in a declaration and send in copies of your unanswered emails and another copy stating she has full custody. State on the bottom that you are aware you can never sponsor your child under family class and to please exempt them from your application.
Not promising it will work, but it worked for us. Good luck!