The question you should ask yourself is who you really are.

Are you one who can adjust and be willing to have two kids (other's kids) into your life? 

If yes, you should step up and set rules for your household and follow through. pre-determined punishment (not abuse) is to be handed out when rules are broken. It's your house so your rules are count. Make sure you hu*****and backs you up all the way. 

If not, get a divorce ASAP.  This is not the life for you.