I co own a new mobile home and I have lived on it for 4 years but the land is owned by my partners mother and my partner lives with me, we agreed to no rent on property not in writing
And you thought that was a good idea?
Sigh.
we have already paid and installed concrete drives and some structures to the property
The worse part of the bad idea.
what rights do I have by law concerning allowing others on my property
All other things being equal, you can invite anybody you want on to or in to the property you occupy. Though if your invitees are doing damage to the land owner's property, that's another story.
can she make us move off the property.
Ultimately, yes. You and your partner are tenants. Your tenancy can be terminated. It would probably require a longer notice period since it's a mobile home.
can the mother control or demand I be removed from the home
If mother convinces daughter to get a restraining order against you then, yes, you can be removed from your own home and it's likely the police or sheriff will remove you with only a few minutes notice.
Beyond that, the mother's attempts to control or demand are nothing but hot air (except for potential termination of tenancy) and you are free to ignore them.
I would hope that your partner is taking your side against the mother. If not, then your relationship is doomed and you'd better come up with an exit strategy that preserves your stake in the mobile home.
Explain how all this strife got started.