I'd like to have a large family with more than 8 sims. Two parents and many children. Do I have to wait until some move out or is there a way to have all the kids in the house at the same time?

Depends on what version of the game and dlcs you have. Base game alone, no more than 8. Base game with Discover University, move out teens and older then invite them to join family again as roommates. You won't be able to to control the roommates, but they will all be under same roof.

If your looking for a scenario like two parents and ten kids, then four kids will have to go live with other grown ups, so that you can invite them back as roommates.

With mods such as MCCC you can have more than 8 controlled sims in household or with the mod Control Any Sim, (found here on MTS) you can take control of roommates, so again more than 8 sims in household.

I have MCCC and have it set for 20 sims in a family but I can't figure it out to get more sims actually in the family.

Check out TwistedMexi's more sims in household mod. It's a bit dated tho.

With MCCC there is another option you need to check to allow you to try for baby in full households. but BE CAREFUL. Even if you have it set to 20 sims, you can only go into CAS with 8 sims at a time. If you try to open CAS with more than 8 sims, any sims after the first 8 will be permanently deleted from the game and cannot be retrieved unless you load a previous save. There is an option through MCCC>sim commands to just open the one sim in CAS alone that you'll need to use.

If the sims you are trying to add to the family are already in another household, you can invite them to the lot, then right click them with testingcheats on and select "add to family"