How do I get the full cost to replace a barn from my insurer?

There is no way to answer this question in the abstract. Insurance policies are contracts; like any other contract, the parties to it are obligated to follow the contract's requirements--no more and no less. Therefore, the first key issue is what kind of coverage do you have? Is it replacement coverage, where the insurer has to pay the cost to rebuild/replace? Or does the insurer only have to pay the "value" of the barn at the time it fell down, which could easily be less than the replacement cost.

Once you know what kind of coverage it is, the next question is whether you agree with the insurer's factual determination. For example, say that it is replacement coverage and the insurer feels it only takes $45k, to rebuild. If that is not the case, you can contest it--insurers cannot arbitrarily determine what to pay, but again are bound by the policy. If the insurer has to pay to rebuild, then you provide documentation of what the building cost would be (e.g. estimates and quotes). If the insurer still won't pay what you deem is appropriate, then you could sue the insurance company to get the additional compensation you feel you are due under the policy--and there are attorneys who specialize or at least are experienced in doing this.

So first, deterimine what coverage you are entitled to; second, compare your estimates under that type of coverage (i.e. replacement cost or value) vs. what the insurer offers; third, document why you feel you should get more and see if the insurer will up its offer; fourth, if all else fails and you think you are owed more, consider a lawsuit.