In general, you can only make one indirect rollover per year, but you can make more than one direct rollover per year. With an indirect rollover, you receive a check from custodian 1 and must deposit it with custodian 2. With a direct rollover, the money is transferred directly by custodian 1 into your account with custodian 2.
Your plan consists of a direct rollover from your traditional IRA to a Roth IRA at custodian 1, then a direct rollover from custodian 1 to custodian 2, so it is permissible to do them both in the same year.
However, as pointed out, you would have to convert the entire balance of your traditional IRA to a Roth IRA and pay income tax on the deductible portion of the traditional IRA.
