Help with X-trees

[learning3nglish]

The sentence is "The monster's mother's lair".
I was able to create a tree for "the monster's mother" but how can I make another possessive 's and noun into this table?

         
                DP
        /              \
    DPi 	        D'
     I	     	       /   \
     D'              D        NP
  /   \	             I        /   \   
 D    NP            's     DP     N'           
 I      I	           I       I
the     N'                 t       N                     
         I                         I      
         N                         mother   
      	 I			       
     monster

Or have I done this tree wrong? I know that a phrase like the student's program it makes more sense to treat the student as an argument of the possessive morpheme rather than of the noun program. Is this the same case?

[Soup]

Look at it this way, the DP monster governs D' mother's lair. In other words,

1. DP branches into DP [monster] and D' ['s mother's lair]
2. D' branches into D ['s] and DP [mother's lair]

3. DP branches into DP [mother] and D' ['s lair]
4. D' branches into D ['s] and NP [lair]