MIL moved in uninvited under false pretenses

Just discoverd this subreddit. We asked MIL to fly over to help with childcare for 2 months since she's retired and we were about to change jobs, nanny, and move to a different state. I am grateful she said she would come.

She said she felt uncomfortable with her home being vacant for 2 months, so she SOLD her home and boxshipped her home to our new house.

Well we were moving from a tiny 2 bedroom apartment to a large 4 bedroom house so I figured we can accomodate her temporarily. She told me before and after the wedding that she wants to move near her son once we settled down and has no intention of living with her son/DIL (me) and I told her I absolutely do not want to live with my mom or MIL in the future.

4 months after the move, she has not looked for a place to rent or buy. I asked my husband what is the deal. He says MIL plans to spend 6 months in china and 6 months in the US every year (she has a greencard so she has to stay in the Us for 6 mo every year). Then i asked "wait, if she's uncomfortable leaving her home vacant for 2 months, how is she going to be comfortable leaving her home vacant 6 months every year?!?"

Turns out, husband and MIL have a different definition of temporary. They think intermittently moving in and out of our home for the next 5-10 years = temporary arrangement!!!

So now I am trying to kick MIL out.

To make matters worse, we moved separately (husband, kid, and MIL first, i came 2 weeks later). Well during the 2 weeks, she moved all her kitchen stuff into our brand new kitchen and my kitchen stuff remains unpacked, in the basement because there is literally no more space.

(We're chinese, unfortunately it's culturally taboo to confront MIL)