A properly drawn will names an executor and trustee and also names an alternate if, for whatever reason, the first person named refuses or cannot fulfill his/her mandate. When both the named and alternate estate trustees are unable or unwilling to act, then someone who has the support of people with a financial interest in the estate should bring an application to be estate trustee with a will.
If there is no consensus candidate or person agreeable to a majority of the beneficiaries and more than one competing person wants to be estate trustee, the court will review all the circumstances and decide. Sometimes a financial trust company will be the compromise choice.
There is no iron rule when more than one person wants to be estate trustee in these circumstances, but normally courts give preference to those closest to the deceased. For example if a spouse, child and grandchild each wanted to be the estate trustee, in order of preference, courts have preferred spouses, then children, then grandchildren.