You asked: "I don't even know what I am trying to ask other than how would I have known the information was incorrect and is there anything I can do besides pay the IRS the amount they say we owe?"
The discussion here is informative, but may not help you if you don't know what actually happened - was the 1099-R actually filled out incorrectly by your company? It seems that it was, but it is difficult even for the excellent tax professionals here to be sure without seeing your documents and asking some additional clarifying questions.
I am assuming that when the IRS wrote you a letter asking for the payment of taxes, that they also added on penalties and interest to the amount? If so - and since you confess a lack of expertise in this situation - I would encourage you to contact a local Enrolled Agent (see https://taxexperts.naea.org/ ) or a local CPA (each state has their own look-up). If the company issuing the 1099-R made errors on the 1099-R, the Enrolled Agent or the CPA should be able to draft a reply to the IRS asking for an abatement (waiver) of at least the penalties due to the company's error.
You have probably seen that the IRS wants a reply within three weeks or so, so don't delay. Even if you can't get professional help soon enough, reply to the IRS stating that you are researching the issue and expect to have a reply to the IRS within another three weeks. Always reply to the IRS in a timely fashion, even if you don't have all the answers yet. Both the Enrolled Agent and the CPA can be empowered by you to represent you before the IRS and to take over the conversation with the IRS and negotiate a solution.
