Why HMS Rodney had no practical postwar future

Did Churchill want to keep both HMS Nelson and HMS Rodney after the Second World War?

No. Nelson was the candidate for retention, while Rodney was so worn out that rebuilding her would have been comparable to building another ship.

Churchill wanted to retain HMS Nelson, not both Nelson-class battleships. Rodney's engines had been driven so hard that keeping her after the war would have required rebuilding most of the ship. The cost and effort would have approached constructing a replacement. In that comparison, another Vanguard-type ship made more sense than trying to restore the worn-out Rodney.