I don't do pacifiers at all for any age. I also don't do blankets, loveys, or any attachment items. What this Mom is doing is intentionally causing an escalation with her child at transition times. The Mom likes the attention and she likes that she wins over your wishes every single day because the kid is HER child not YOUR child so she will decide and YOU will DO. Do as you are told "do".

I would tell her straight... do not bring that into my house. I don't want bottles or his binky. You can have them all the way to my driveway at drop off and all the way home after you pick up but not IN my house. She's pushing you around. Plain and simple.