We often play by dealing 2 of each. Look at all 4 and keep the mama & papa that you want.
We deal out four Mama and Papa cards.
We choose from our Mama cards first and then take the coordinating starting cards. When we choose from visitor cards, we pick two and keep one or if the situation arises where we get to keep two, we choose three and keep two. Return the unused card to the bottom of the deck. We do this throughout the game, as well.
We find it helps minimize luck of the draw a bit. (It can also lengthen the game a little as there is often a pause between turns to decide when card to take.)