CNN model conditional layer in Keras

Thanks a lot for reading my post.

I am trying to build a conditional CNN model. The model is,

At the first stage of my model, I feed my data to Model 1 then, based on the prediction of Model 1, I want to train the model to Conditional Cat model or Conditional Dog model and finally, give the output from Conditional Cat model or Conditional Dog model. How Can I do this?

Note: My effort is,

import keras
from keras.layers import *
from keras.models import *
from keras.utils import *

img_rows,img_cols,number_of_class = 256,256,2
input = Input(shape=(img_rows,img_cols,3))

#----------- main model (Model 1) ------------------------------------
conv_01 = Convolution2D(64, 3, 3, activation='relu',name = 'conv_01') (input)
conv_02 = Convolution2D(64, 3, 3, activation='relu',name = 'conv_02') (conv_01)

skip_dog =  conv_02

conv_03 = Convolution2D(64, 3, 3, activation='relu',name = 'conv_03') (conv_02)

skip_cat =  conv_03

conv_04 = Convolution2D(64, 3, 3, activation='relu',name = 'conv_04') (conv_03)


flatten_main_model =  Flatten() (conv_04)
Output_main_model = Dense(units = number_of_class , activation = 'softmax', name = "Output_layer")(flatten_main_model)


#----------- Conditional  Cat model ------------------------------------ 
conv_05 = Convolution2D(64, 3, 3, activation='relu',name = 'conv_05') (skip_cat)
flatten_cat_model =  Flatten() (conv_05)
Output_cat_model = Dense(units = number_of_class , activation = 'softmax', name = "Output_layer_cat")(flatten_cat_model)

#----------- Conditional  Dog model ------------------------------------ 
conv_06 = Convolution2D(64, 3, 3, activation='relu',name = 'conv_06') (skip_dog)
flatten_dog_model =  Flatten() (conv_06)
Output_dog_model = Dense(units = number_of_class , activation = 'softmax', name = "Output_layer_dog")(flatten_dog_model)

#----------------------------- My discrete 3 models --------------------------------
model_01 = Model(inputs = input , outputs = Output_main_model,name = 'model_main')
model_02_1 = Model(inputs = input , outputs = Output_cat_model ,name = 'Conditional_cat_model')
model_02_2 = Model(inputs = input , outputs = Output_dog_model ,name = 'Conditional_dog_model')

How can I merge these 3 models (model_01, model_02_1, model_02_2) based on these conditions?

Conditions are:

1. Feed data to model model_01
2. based on model_01 result feed data to model_02_1 or model_02_2
3. Next, predict the final output from model_02_1 or model_02_2

from CNN model conditional layer in Keras