There is no such thing as a "standby guardian" under Michigan law. You are either a legal guardian or you are not. It is not clear from your summary whether your nephew even has any rights, in this matter, since he is arguably not the legal guardian of the children. As a biological parent, he would be considered the "natural" guardian, and he would have parental rights. In that case, he would have the right to delegate those rights, for periods of up to 6 months, at a time, on a temporary basis. This is usually done by way of a Power of Attorney form.
If your nephew were to pass away, there would need to be a probate proceeding to appoint legal guardians and conservators for the children. The surviving biological parents, if any, would need to be given notice. Such persons would have rights superior to anyone else. The "next in line" would be those persons "nominated" by a biological parent. In any event, appointment could only be done through a court proceeding, and it would not be automatic.
The court would most likely appoint a guardian ad litem to interview all of the parties and to make a recommendation to the judge. The judge would decide who to appoint, on the basis of what is in the children's best interest.
This means that your nephew, assuming he has parental rights, can designate you in one of two ways: by Power of Attorney, (which is effective only during his lifetime), or by a Will (or some other substitute), which would state a "preference" upon his death. He can do this, and *should* do this. But you may still be in a for a serious battle, if there is someone else who wants custody of the kids or their assets, upon your nephew's death. (The assets are probably another matter, entirely, and the nephew may be able to tie those up very effectively, which he should do, in order to eliminate any financial incentive for someone to seek custody of the children.)