I am not sure whether the way you are parsing the sentence is correct. I am sure that there is a different way to parse it.
This is like your teacher telling you [that] you’ve done well and allowing you to skip a grade.
There are two phrases beginning with -ing words. These -ing words could be gerunds, or they could be participles. If they are participles, then the participial phrases must modify something. In this sentence, they can modify "teacher".
The preposition "like" needs an object. If the -ing words are participles, then they can't be the preposition's object. However, the word "teacher" can be the object of "like".
As I parse the phrase, the preposition "like" takes the first available object, "teacher". The genitive pronoun "your" modifies "teacher". The two participial phrases also modify "teacher".
When the phrase is parsed in this way, we can still consider "teacher" to be the actor of the participles, but we do not consider it to be their subject. It's just the thing that the participial phrases modify.
Regardless of whether we consider the -ing words to be particples or gerunds, they each start a complete phrase. Within the first phrase, the pronoun "you" is the indirect object of "telling", and the nominative subordinate clause "[that] you've done well" is the direct object. Within the second, the pronoun "you" is the direct object and the infinitive phrase "to skip a grade" is the object complement.
It doesn't make much sense to separate "telling" from the rest of its phrase.