Ice cream pudding cake rethought

I've been thinking about the ice cream pudding cake I made for my birthday. It was yummy, but there was a problem. I put the cake in the freezer to make it firm and the pudding was VERY frozen; even after letting it sit on the counter for an hour. So I put it in the fridge and the ice cream kept melting. I think next time I will pick either pudding or ice cream. That way I will be able to enjoy it without freezing my teeth or hurting my hand cutting it or dealing with melted ice cream all over everything.