Two stack sorting

JavaScript (ES6), 23 bytes

Uses 1-indexed cards and stacks. The initial stack is the 1^st one. The single-card stack is the 3^rd one. Expects \$0\$ for an empty stack.

Returns a 2-digit number, where the 1^st digit is the source stack and the 2^nd digit is the destination stack.

(a,b,c)=>c?b>c?21:32:13

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Commented

(            // input:
  a,         //   a = top card in the primary stack
  b,         //   b = top card in the secondary stack
  c          //   c = card in the temporary stack
) =>         //
  c ?        // if there's already a card in the temporary stack:
    b > c ?  //   if there's a card in the secondary stack and it's
             //   greater than the temporary card:
      21     //     move from secondary to primary
    :        //   else:
      32     //     move from temporary to secondary
  :          // else:
    13       //   move from primary to temporary

Jelly, 9 8 bytes

ṖM⁸aḢ;‘$

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A monadic link taking a list of three integers representing the top of the three stacks, or zero for an empty stack. The three stacks are [single card, destination, source]. Returns a pair of integers indicating which stack to move from and to. In keeping with Jelly’s indexing of lists, the third stack can be referred to either as 3 or 0.

Inspiration taken from @Arnauld’s JavaScript answer so be sure to upvote that one!

Explanation

Ṗ         | Remove last list item
 M        | Indices of maximum
  ⁸a      | Original argument and with this
    Ḣ     | Head
     ;‘$  | Concatenate to itself plus 1