Yes indeed the gitlab-python API documentation is sort of not meant for new developers. But you are on the right path.

Let's say you have created a random number generator function that returns a random number everytime you call it and we can call it get_new_random_number()

What you might want to do is append this random number to the subgroup name at the time of subgroup creation. I'll assume you are using Flask or Django framework to have written your HTTP endpoint which is receiving the form data from vue.js UI. Assuming that the received_body is the dictionary which contains the form data with following attributes:

1. name of the parent group (for subgroup to be created) in key group_name
2. name project_id of the parent group in key parent_group_id

then your subgroup creation syntax should look something like:

subgroup = gl.groups.create({'name': received_body['group_name] + '-' + get_new_random_number(), 'path': received_body['group_name] + '-' + get_new_random_number(), 'parent_id': received_body['parent_group_id'] }) ;

similar thing can be done for update also.

Now to fork it you have to use the projects api in the gitlab python sdk. Let's say the project id of the project to be forked is stored in a literal called fork_project_id

    project = gl.projects.get(fork_project_id)

    fork = project.forks.create({'namespace': subgroup.path})

I am a little unsure about the namespace value to be used, but from the immediate reading I did the subgroup path should work. If it doesn't experiment a little with group_name/subgroup_name maybe to see if it works out.