Hi Maggierose,
That is a tricky situation, but there are some things you can do to overcome it.
First is to set the tone for your entire team by staying above the negativity and keeping your message professional. That means keep the conversation focused on the task at hand and keep it consistent for all of your employees, not just the ones you have a good relationship with.
Second is to ensure there are clearly defined objectives for your team, as well as both team and individual goals with milestones they need to reach, and that you can use to manage them with.
This process of setting team and individual objectives, along with timeline expectations should be formalized in writing, presented to your entire team and then followed up in one-on-one discussions with each team member.
Here's the thing. No matter what perspective your boss has, she can't argue with you managing your team in a way that achieves business goals. She should not be favoring your employees, period. She's wrong, but having that conversation with her is probably not going to get you anywhere today. Instead, if you keep her updated on your focus as a manager and use her to focus on business issues where your team (as a whole) needs support, then the problem will resolve in one of two ways.
1) she will start being more responsible as a boss and focus on helping you achieve business goals.
2) she will try to work against you, because you are focused and driving your team outside of her control.
Either way, you will be doing the right thing for your company. If people don't meet milestones, they are letting the entire team down and you have documented proof for performance reviews and possible termination. The key is to use this process to get each of your employees onboard with what you and the team are trying to collectively achieve. Your two negative employees may become great assets during this transition..and that should be your goal, to engage all of your team.
Right now you are trying to fix the problems in your team. What I'm suggesting is that instead, you focus your team on achieving objectives. The rest will work out on its own.
We've all been there with employees that may not like us, the important thing is that they respect what you are trying achieve and participate in helping you do it. When you have one-on-one discussions be clear about this point. Focus on clear goals and be supportive. Set an example for your team, and your boss.
I hope this helps. Please keep us posted on your progress.
Lisa