Can my sister who has poa of my mothers living trust kick me out of the house?

Chances are yes, but you need to tell us a LOT more than this.

If you are not an owner of the house, then yes, the person who controls the property can have you evicted. They can't just kick you out. You have to be legally evicted.

If your mother is still alive. And your mother has a living trust.

Of is the living trust, to you, for your life?

You will need to clear up. In whose name the trust is in,

But if it is the mothers trust, and the sister has POA, and the mother is alive, the sister may kick you out, unless you talk to your mother and your mother says no.
A POA merely signs or acts for the other person, but the other person is still in control.

We really need to know if your mother is still alive and that will tell us more about the status of what is going on.

... poa of my mothers living trust ...

You are mixing apples and oranges here. A trust, whether an inter vivos "living trust" or a testamentary trust (created in a will and thus effective at death of the trustor) is controlled by the trustee. A power of attorney, on the other hand, merely gives the recipient (the attorney in fact) the power to act in behalf of the principal. So a POA ends with the death of the principal, if it has not been revoked previously.