Retirement tax questions

If the IRS only recognizes 1 of the 3 distributions from the Prudential IRAs as a rollover to another traditional IRA, then yes, I'd be paying double taxes on the other 2 distributions if I were to convert them to a ROTH.  And if I don't convert them to a ROTH then I (or my heirs) would be paying taxes on those 2 distributions again when they are finally withdrawn from my traditional Vanguard IRA. Either way, not a good outcome.  The funds are in cash in my brokerage account so no capital gain/loss and no impact on my 1099B.  I am really ticked off that Vanguard led me down this path and am hoping that they can fix things. I am also mad that I let myself get into this predicament.