Have you read any books on polyamory or listened to podcasts about it?
I would recommend looking at the following: Unicorns-r-us.com The Multiamory podcast Some book suggestions: Opening Up, More Than Two (there is massive controversy around one of the authors, but it's still a very solid book to most), or Love in Abundance
I will warn you that with what you just wrote, a lot of these may make you feel attacked. I hope you're able to look past that, absorb, relook at your post, and see if you still have those questions or if you have new ones now.
My first question is: what are y'all doing? I can't tell how much work either of you has put into learning about polyamory, learning about how to be good hinges and take care of all of your partners or anything else related to polyamory. Additionally, I am getting the feeling that both of you are doing "the relationship with the person I'm living with always comes first" thing. Or that you and Cheddar are primaries with nobody else being a primary partner to either of you. If that IS the case, I hope you're being up front about it.
Both of you need to be thinking about if your relationship with each other is meeting your needs. It doesn't necessarily matter what your metas are"getting". Are you "getting enough" from each other? Do you know what "enough" is? Are you both mature enough to have figured out your enough for yourselves based off of your actual needs and wants vs "I need everything that is important to me + I have to be first/always get anything my meta gets, not because I actually want or need it but because it makes me feel bad when they get things I don't".
It sounds like you both need to work on repairing your relationship. Separately, I think you both need to decide if polyamory is really for you, and start digging into podcasts & books about it, because it seems from your post that neither of you has done a lot of the foundation work that helps make polyamory successful and healthy.
Cheddar's partner has every right to be pissed and not talk to her. A LOT of polyamourous people have no interest in dating someone who allows their preexisting partner to veto or put limits on their relationships. If you and Cheddar are going to practice polyamory like that, you need to inform prospective partners of it up front, and look for people who will agree to a relationship like that.
Get some polyamory resources. Read them, listening to them, communicate. Figure out what you each need from your relationship and see if you can give each other that. Make sure polyamory is right for you, for both of you.
Those things may or may not help your current attempted relationships, but they will definitely help your future ones.