Let me add some clarity. It all depends on what the will says about a named beneficiary predeceasing the testator. If certain language was used (e.g., "per stirpes") then the children (technically "issue") of the deceased beneficiary WOULD step into the parent's shoes for the allocation of assets that would have gone to the beneficiary if they had not died before the testator. However other lingo in wills sometimes have a different result if it says the bequest go to "living" beneficiaries at time of death which means the children (in your fact pattern) would NOT get anything that had been earmarked for the deceased beneficiary. Only reading the will can answer you which way it goes.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.
John P. Corrigan's answer is correct. I would just add though that if the Will is silent and does not indicate that the share passes to the children or is divided among the other beneficiaries, than state law is used to determine who are the contingent beneficiaries.
Who receives the assets will depend on what the Wills says regarding the beneficiary or what happens if that person is dead or doesnt take for some reason. If the Will is silent and has no residue clause then it will depend on the relation of the testator and the beneficiary.
Regardless, the administrator is the person who is empowered to act. Being administrator has nothing to do with beneficial rights.
As to your question, the person named as executor/administrator can contest the Will but not as administrator. That is internally inconsistent. How can you challenge the same document that you claim entitles you to serve as administrator.
You need to contact a probate attorney to determine how to proceed and determine if you have grounds for contesting the Will and determining who the remainder beneficiaries are.
The general advice above does not constitute an attorney-client relationship: you haven't hired me or my firm or given me confidential information by posting on this public forum, and my answer on this public forum does not constitute attorney-client advice. IRS Circular 230 Disclosure: In order to comply with requirements imposed by the Internal Revenue Service, we inform you that any U.S. tax advice contained in this communication (including any attachments) is not intended to be used, and cannot be used, for the purpose of (i) avoiding penalties under the Internal Revenue Code or (ii) promoting, marketing, or recommending to another party any transaction or matter addressed herein. While I am licensed to practice in New York and California, I do not actively practice in New York. Regardless, nothing said should be deemed an opinion of law of any state. All readers need to do their own research or pay an attorney for a legal opinion if one is necessary or desired.