The term "trustee" refers to the company holding the IRA account because IRA accounts are actually trusts under the tax code. The term "trustee" is used interchangeably with the term "custodian." A "trustee-to-trustee transfer" is roughly equivalent to changing investments within an IRA since it represents neither a reportable distribution from the old IRA nor a reportable rollover to the new IRA.
A code 4 Form 1099-R issued to your wife with an amount in box 1 equal to the full value of the IRA implies that the entire IRA was distributed to your wife, not moved by trustee-to-trustee transfer. Because your wife is a non-spouse beneficiary, such a distribution is not eligible for rollover and TurboTax will not permit indicating that the distribution was rolled over.
Handled properly, the RMD would have been paid to your wife and only the amount of the RMD would appear in box 1 of the 2018 Form 1099-R. The rest should have been moved to the inherited IRA at the new investment company by nonreportable trustee-to-trustee transfer, so the amount that was moved should not be in box 1 of any Form 1099-R.
Presumably your wife's father died in 2017. One of the 2017 Forms 5498 is apparently reporting the date of death fair-market value and would have been issued to your wife's father. The information on this Form 5498 is useful for valuing the asset if the decedent's estate is subject to federal or state estate taxes or there is state inheritance tax. The other 2017 Form 5498 would have been issued to your wife showing the 2017 year-end value needed to calculate her 2018 RMD. These do not have anything to do with the movement of the inherited IRA. (In my answer I had assumed that these were 2018 Forms 5498.)
