some of the initial ideas i can think of would most likely be along the lines of mr birling having authority in his own home, but mrs birling also having quite a lot of control over her children, and id probably talk about how sheila appears to have the least amount of control, as a woman and because of her age.
obvs eva didnt have any control whatsoever, she had to rely on her job, then on gerald, then on mrs birling, but she probably didnt have any choice but to agree to sex with gerald, because who knows what'd happen if she didnt.
id definitely talk about the inspector, how he almost immediately creates a sense of "massiveness" and almost takes away mr birlings authority, who seems to be intimidated by the control the inspector has over the family when it comes to stopping arguments, and his control over his investigation, how he does things "one at a time", etc.
however, the inspector is also there to give power to those who dont have it. as mentioned earlier, sheila has the least amount of power/control in her family, but the inspector helps her to come out of her shell a bit, and she has the confidence to be more independent, to not be infantilised, and acknowledge she doesnt need to rely on gerald, and that she can make her own way in life.
ofc, sheila did have control over eva smith, beacuse of her privilege in terms of family status. priestley tells us that in the current society, control correlates with privilege. for eva smith, it was too late, but, through the inspector, sheila learns that although other members of her family have more control than her, she also has a significant amount of power, and she realises how important it is to use it wisely, due to the influence it has over others.
obvs this isnt a complete essay, but its just some ideas id consider talking about. hope this helps!