Should she be disciplined? Of course but you also need to figure out the why here.
This was a mare who was very well behaved before and has started to be very disrespectful. I suspect there have been some handling and rider errors along the way that have gradually taught this mare that acting this way is acceptable, however they were small things at first that went pretty much unnoticed.
Is she sore anywhere and does her saddle fit properly? Those two things can make even the best horses act out.
Next, how do you mount?
Correct: Notice that Warwick is close to the horse and grabs mane and saddle horn. He steps up then swings his leg over. When he is halfway on, he's over the horses center of balance, thus giving the horse no reason to move.
And of course I can't find a video when I need it on an incorrect way. However I see many many people mount by grabbing the saddle horn and the cantle, thus standing perpendicular to their horse. They then get their foot in the stirrup and pull themselves on. This completely unbalances a horse, causes a saddle to roll and digs that saddle into the shoulders of the horse. Even a well trained horse often moves when people mount in a similar way to this. Over time that can progress to making a horse fore and the horse getting progressively more irritated about a rider mounting.
All of that said, just slapping your horse is doing no good as you are finding out.
Instead, put those feet to work, ASAP as soon as you even see an ear pin. Put your horse in a rope halter if you have one with a long training lead. Now go through your mounting steps. Can you get to your horses barrel without her getting pissy? Can you place your hands in the appropriate spots? Can you raise your foot to the stirrup? Can you place your foot in the stirrup? Can you step halfway on? Can you swing your leg over?
When you find the point that the answer becomes no and she even thinks about kicking, go to her butt using your leadrope in your right hand and whack her on the butt, making her hindquarters move away from you, when she is moving calmly and not in a irritated fashion, let her rest. During this, keep your left hand at about shoulder level, so if she goes to run her shoulders into you, you can use your hand to send her back out. Then try again.