“freeze” some variables/scopes in tensorflow: stop_gradient vs passing variables to minimize

The easiest way to achieve this, as you mention in your question, is to create two optimizer operations using separate calls to opt.minimize(cost, ...). By default, the optimizer will use all of the variables in tf.trainable_variables(). If you want to filter the variables to a particular scope, you can use the optional scope argument to tf.get_collection() as follows:

optimizer = tf.train.AdagradOptimzer(0.01)

first_train_vars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,
                                     "scope/prefix/for/first/vars")
first_train_op = optimizer.minimize(cost, var_list=first_train_vars)

second_train_vars = tf.get_collection(tf.GraphKeys.TRAINABLE_VARIABLES,
                                      "scope/prefix/for/second/vars")                     
second_train_op = optimizer.minimize(cost, var_list=second_train_vars)