If we own a farm and let a family member live on it but now they are talking about taking the land through squatter's rights, is there anything we can do about it?

There is no such thing in the United States as "squatters rights"--some European nations recognize these, but we do not. What we do have is "adverse possession," which in very rare instances can allow someone to claim land; however, and this is critical, "adverse possession" must be ADVERSE--that is, it cannot be with the land owner's permission or approval. If you give someone the right to live in your property, they cannot claim it, no matter how long they live there.

However, since it appears these people do not appreciate what you are doing for them and may try to cause trouble for you (e.g. even if they'd lose an adverse possession case, they could try to file one and force you to spend money and time defending it), you should probably remove them. If they are paying rent, they are tenants, and have to be evicted as tenants; if they are not paying rent, they are guests, and you can ask them to leave at any time--and bring what's called an "ejectment action" to remove them if they won't go. You should speak with a real estate or landlord-tenant attorney about removing them.