Who is the Executor of your father's will? He or she would bear the primary responsibility for making sure taxes are collected. As for whose share bears the taxes, an attorney in your father's state would need to review the will and, possibly, that state's statutes, to determine the answer. Good luck to you.
This information is presented as a public service. It should not be construed to be formal legal advice nor considered to be the formation of a lawyer/client relationship. I am licensed in Connecticut and New York and my answers are based upon the law in those jurisdictions. My answer to any specific question would likely be different if I were to review a client's file and have the opportunity to interview the client. Accordingly, I strongly urge you to retain an attorney in your jurisdiction with respect to any legal matter.
This is an excellent question and one that requires an attorney to assist you. These tax issues when the "tax allocation" clause is bad are rather common these days. I cannot speak for MN but in NJ I dealt with a similar case and the brunt of the death taxes were borne by the beneficiaries of the individual assets on a pro-rata basis (there was nothing in the residue, it was all either specific bequests in the will or joint/beneficiary property).
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
You need to contact a probate attorney in the state where your father died domiciled to determine what action to take. Generally during the administration of the estate the expenses in question are paid from estate assets but an attorney needs to read the will to determine this and may need to research the matter.