Good that you caught this. That the Vanguard rep suggested rolling these over to a traditional IRA first suggests inadequate training on their part. Even if there was no limitation on rollovers, there was no reason to turn one transaction into two.
One of the distributions from the original Prudential traditional IRAs was eligible for rollover (assuming no other previous rollovers within the limitation period), so I think that one should stay in the Vanguard traditional IRA to be converted from the Vanguard traditional IRA to the Vanguard Roth IRA; I don't think that a permissible rollover is permitted to be distributed as a return of contribution. Because the other two distributions from the Prudential IRAs were ineligible for rollover due to the limitation on rollovers, these two constitute regular traditional IRA contributions that will need to be distributed by an explicit return of contribution. Within 60 days of the distributions from Prudential you'll need to complete the indirect conversion of these other two distributions from Prudential IRAs directly to the Vanguard Roth IRA as you originally planned, independently of the returned contribution, using whatever source of funds you choose.
