I'd tell the executor to contact the attorney regarding any issues they have over the appraisal for estate purposes. Not your circus, not your monkeys - the executor deals with the estate only, and once the property is yours they have no interest in it or in any appraisal on it for your future tax purposes. Similarly, your interest in the appraisal has nothing to do with the estate or the executor but is for your personal tax purposes only, and for tax purposes I think you should be entitled to rely on the appraisal provided to you - although you may want to check with the tax authorities that this is OK if there are valid doubts about it.
Can the relatives pay anything towards this transaction? I understand gifting a property that has been inherited, but why should it cost you money to do so? If possible, get the relatives to pay both the capital gains and the transaction costs.