1099R needs splitting into Distribution and Rollover

Briefly, after taking an aggregated RMD from one of two IRA accounts, a rollover of the remaining funds had to be done to another custodian in order to do a Roth conversion prior to Dec. 31.   We were directed to fill out a form for a full surrender of the IRA with check being sent to us then immediately rolled over into another IRA at another custodian.  The rollover to the new custodian was classified as a rollover by them, however, the initial custodian, although being told that the surrender was to be a rollover, treated it as a normal distribution.  The reason we had to get a check instead of doing an electronic rollover was that it was mid-December and the standard process would have taken past Dec. 31.

 

So, the ONLY taxable distribution was the RMD (minus some QCD) whereas the 1099 shows the entire IRA distributions from the account are taxable.  How can this be managed, with an explanation to the Fed and State?