We were going to be married, been here 8 years and he threw my 2 year old grandbaby out last night and me today. Do I have any rights?

You cannot be ejected from your residence without going through the proper legal process of eviction. You can go to the police and prove this was your residence and move back in. But if he owns the residence, then he can legally get you out usually within 30-60 days.

Since this appears to be more of a legal question I've moved it from the Relationships forum. ANY question on law needs to include your general locale as laws vary by area. What exactly transpired last night?

Depending on where you live, you have rights as a tenant only, and have to be formally evicted, unless you committed some act that allowed him to get a restraining order. What state are you in, if the US?
The grandchild is another matter, and would depend on how long he's been there.
If you were married, he couldn't throw you out at all.

Who owns the property ? If rented whose name is on the lease?

If he owns it, or the rental is in his name alone, he may evict you, He will have to give you formal notice. He can not throw anyone out same day.

... he threw my 2 year old grandbaby out last night and me today ....

I can see the possibility of throwing a 2-year old out, but as a grandparent you must weigh considerably more than your grandchild. He must be very powerful in order to throw you that far.

Seriously, what do you mean by "throw out"? Did he insist that you leave? He can do that.