I have do wish to skip a level. The game just tried to force me to do that because I am full of that type of card but still drew one in the daily card draw. I had to close out the game and restart it.

Why does the game forget a regular map if you hop out of it to check your idle progress. It makes playing the larger maps a chore due to you have to put the Idle side of things on hold until you finish it.

If you pick up a skip level power in the daily freebie when you are already "full" (5/5) it forces you to use (waste) it. it offers you the choice to immediately skip to the next level or ignore it - most of the time you don't want to give up the progress you already made and therefore you DONT want to skip to the next level otherwise you lose winning the full level AP.
bottom line, just stay on the current level, dont skip to the next level.
hope that makes sense.

The game just tried to force me to do that because I am full of that type of card but still drew one in the daily card draw.

When that happens, the game tells you that you unlocked a new level, and asks you whether you want to start it now.

You can just click no.

When your skip level is full, just skip it. Or even superpower skip it. Just don't play it.