I have a very difficult colleague ... She has constantly undermined me and made the office atmosphere very toxic. This has been going on for 2 years now.
Now she's publicly and repeatedly accused you of lying.
What a bunch of absolute WIMPS you work with /for.
Despite the fact she's created a toxic atmosphere for two years they've done naff all to deal with her.
Now they're trying to pile the load of performance managing and behavioural consequences for her into your shoulders?
Tell them exactly what she's been doing and the effect it's had on colleagues, morale, team spirit, productivity, and how long she's been allowed to do it.
And she has now been repeatedly slandering your reputation.
Get statements from supportive colleagues if you can.
Present that to them and ask if they really think it's your job to make that decision??
They are passing the buck and ducking out of their responsibilities.