AITA my gf thinks it's double standards with my son

I've been with my (33 f) gf (29f) for 2 years, we moved in together before covid hit. She has a beautiful 5 year old girl who I love fiercely and I have a wonderful boy who's 13. I have basically been a single parent to my son since he was 1 and was strict on him as a child. Wouldn't tolerate tantrums or would not take any cheek off him (never once have I raised a hand to him, it was just the tone I used) he is a wonderful, polite and kind young teenager now. Her little girl is a normal 5 year old, pushing her boundaries trying to get what she wants. Though I feel she pushes them more with me. If she is rude, nasty, cheeky to me I don't put up with it. My partner supports me in my parenting style with her daughter. but there times when she has felt my son has been rude or cheeky. Some of these times I have felt that its just been a case of misunderstanding between the both of them, but she hasn't then we end up arguing because she sees it as double standards between how I treat the 2 children. We both love the kids so much and I don't want to be unfair on her daughter but I feel she needs tough love sometimes, which is what I gave my son. AITA? via /r/AmItheAsshole https://ift.tt/2GUjQvS