Could you explain what exactly the home has done?
Can you also explain exactly what your mother-in-law has done?
Does your mother-in-law have full mental capacity?
What do you want to achieve?
I hear what you say when you are saying that she treats everybody badly (not unusual with elderly people I understand) and does not single out any ethnic minorities but they feel singled out.
However I’m not certain who has been told not to speak to staff. You or your mother-in-law?
You are free to speak to who you like!
I find the allegation of the manageress somewhat bizarre. As I said earlier, you are entitled to speak to who you like. You don’t break any employment law.
If the employer feels that their staff are being bullied by you, the employer is in breach of its duty to prevent bullying but that is an issue for the manager not for you.
Apart from harassment or banning you from the premises (very difficult to do if your mother-in-law is in residence) I cannot see what actions they can bring against you except to allege that you are harassing the staff but then, the action would be by the staff against you by the management against you.