Stand your ground ??
Lets see - her family has LEASED the land from the Feds for grazing rights-- It is NOT her land or her families- it is yours and mine - the feds lease it to her family for cash... The Mineral rights are not her's or her families either, they belong to the public - and the Feds LEASE to mineral rights - for cash - if wells are drilled the Govt (you and I) get a percentage of the Oil and Gas  - plus taxes etc....
So I am not sure how she is "standing her ground" she may think it is her land - just like I think Rocky Mountain Park is my land --- but that doesn't make it so...
Adverse possession ?? Give me a break - she and her family have leased the land for years - which means it is not hers --- I guess by that logic and rancher who leases Fed land to graze could claim it is their land - OR you could claim a rental house as yours.
Graze the land - but be legal..
out