import tkinter as tk
from tkinter import ttk

class Channel(tk.Frame):
    def __init__(self, parent, *args, **kwargs):
        tk.Frame.__init__(self, parent, *args, **kwargs)
        self.parent = parent
        self.btn = tk.Button(self.parent, text = 'click me', command = self.change_green)
        self.btn.pack()
    def change_green(self):
        main_window.channel_1.btn.config(bg = 'green') # line 11


class MainApplication(tk.Frame):
    def __init__(self, parent, *args, **kwargs):
        tk.Frame.__init__(self, parent, *args, **kwargs)
        self.parent = parent
        self.tab_control = ttk.Notebook(self.parent)
        self.tab_1 = ttk.Frame(self.tab_control)
        self.tab_2 = ttk.Frame(self.tab_control)
        self.tab_control.add(self.tab_1, text = 'tab 1')
        self.tab_control.add(self.tab_2, text = 'tab 2')
        self.tab_control.pack(fill = 'both', expand = 1)

        self.channel_1 = Channel(self.tab_channel_1)
        self.channel_2 = Channel(self.tab_channel_2)

if __name__ == "__main__":
    root = tk.Tk()
    main_window = MainApplication(root)    # <<<< here defined main_window
    main_window.pack(side="top", fill="both", expand=True)
    root.mainloop()