There's a lot to be said for body posture and smiling...and that it comes through in all of our contact with our customers. There are also some new studies on slouching, that it is a more natural form than what we have been taught. Personally, I never minded slouching (even partake in it myself), as long as the smile, motivation, cooperation and willingness are in place. (And as long as the environment is not in the front line of customers).
For me, and please know this is not personal, being new at supervision is the key here. It is somehow embedded in our genetic and cultural make-up that we need to be liked. Management and being liked can be two very different things. You are there to manage the workforce, not to be named most popular. Even if inflicted with a form of sleep apnea, falling asleep on the job is intolerable behavior. There are remedies for apnea, and there must be consequences for inappropriate business behavior.
The key to management is to address issues immediately, appropriately, professionally. Say what you mean, but don't say it mean. And follow through. Let's face it, we are all adults here. Accepting the role of babysitter as manager simply should not suit us.
What does your office enviroment look like? Is it conducive to performing the work required for the business you are in? Do employees have the tools they need to get the job done? Are there opportunities for them? Does your organization provide training and development? Does your department need additional training? If providing excellent service to customers, being part of a dynamic and functional team, having opportunities to develop and grow, AND getting paid for it are not enough motivation, perhaps the employee(s) should consider a different profession.
Assuming the staff is appropriately trained (or training is available), that the environment is conducive to the required work, etc., I would quit asking if more work is required. What else should I expect but a negative response? I would assign work, with deadlines, and I would be sure to follow through. I would remind that this is a place of business, and appropriate, professional behavior is required. I would have no problem writing up offenders, and considering further action if required.
There are plenty of great resources for you, to help and support you as you learn and grow in your position. Seek feedback and support from your manager, and use your search engines. Training, books, seminars, professional organizations, etc. I would suggest leadership development as a primary initial theme.
Good luck to you,