I bred my alpha pair and two other wolves this season. The two betas gave birth before the alpha female and suddenly all of my slots in the den were filled. When the alpha female gave birth the babies didn't show up. Are they saved in the system somehow? If I sell/get rid of some wolves will they show up?

No, those pups are sadly gone.

You can buy more den space though at Realm < Marketplace < Barter

Click Apples and then scroll to the Den Expansion.

Bummer.