enterprise geodatabase - Efficiently selecting related records using ArcPy?

Below is the code I'm using to replicate the "related tables" button in ArcMap. In ArcMap that button selects features in one feature class or table based on the selection of features in another related feature class or table.

In ArcMap I can use that button to "push" my selection to the related table in a matter of seconds. I was unable to find anything built in to arcpy that replicates the button so I used some nested loops to do the same task.

The code below loops through a table of "treatments". For each treatment, it loops through a list of "trees". When a match is found between the ID fields of treatment and trees, a selection occurs in the tree layer. Once a match is found for a treatment, the code does not continue to search the tree layer for additional matches. It goes back to the treatment table, selects the next treatment and again searches through the tree feature class.

The code itself works fine, but it is agonizingly slow. The "treatment table" in this case has 16,000 records. The "tree" feature class has 60,000 records.

Is there another more efficient way to recreate what ESRI is doing when it pushes the selection from one table to another? Should I be creating an index for the tables? NOTE: This data is stored in an SDE.

 # Create search cursor to loop through the treatments
treatments = arcpy.SearchCursor(treatment_tv)

treatment_field = "Facility_ID"

for treatment in treatments:

    #Get ID of treatment
    treatment_ID = treatment.getValue(treatment_field)

    # Create search cursor for looping through the trees
    trees = arcpy.SearchCursor(tree_fl)
    tree_field = "FACILITYID"


    for tree in trees:

        # Get FID of tree
        tree_FID = tree.getValue(tree_field)

        if tree_FID == treatment_FID:
            query = "FACILITYID = " + str(tree_FID)
            arcpy.SelectLayerByAttribute_management(tree_fl, "REMOVE_FROM_SELECTION", query)
            break