I have not seen your prior posting so forgive me if I touch on something that was already covered.
As far as your stepdaughter is concerned, remember that her relationship with her father should not be in competion with your relationship with your husband. Your husband should back you up regarding personal conversations between husband and wife. They are none of her business. If she cannot stay out of your conversations, could you wait to have important talks behind bedroom doors just like you would around a child over the age of 5?
What about posting a chore chart for everyone in the house. Even if you feel like your stepdaughter acts like a teenager, she does not need another mother so you cannot enforce rules by treating her like a child. With a chart, everyone feels like they are a part of the family, your younger children can visually see that everyone takes part in the day-to-day upkeep of the house, and your stepdaughter feels as if she is included.
Regarding your husbands surgery, try to feel grateful that you have another set of hands to help you with things. Try to let her feel like she is helping instead of being in the way. Bottom line, she loves her dad. You love your husband. Take her to lunch. Try to build a relationship with her and look at her as a friend. Would you speak openly with your friends in the kitchen....probably not.
Good luck!