What the IRA is invested in and where it is housed is totally up to you HOWEVER the inherited non spousal IRA must retain the correct name and cannot be co-mingled into an non inherited IRA... it must always be listed as an inherited IRA ... talk to the IRA custodian for the correct verbiage.
And an RMD cannot be rolled anywhere ... it must be distributed and taxed as ordinary income. However if you are eligible to make a deductible IRA contribution then it may offset the distribution on the tax return as an adjustment to income. And RMD on an inherited IRA is never subject to the 10% penalty because the code in box 7 or the form 1099-R will always be a 4 .. which is why the IRA must remain in the deceased name.
