OP, I didn't call you pathetic, I said that the level of possessiveness by some parents over their children is pathetic, and I stand by that.
It is entirely understandable that in a moment of madness, a parent would feel sad at the realisation that another woman (or man) might have a parenting role in the lives of their children. But if you think about it for a minute, what is the alternative? Hoping for a step parent who is the devil incarnate and who the children can't stand? Hoping for someone who is horrible to the children or who refuses to have anything to do with them? Is that in the best interests of the children? Or of the resentful parent?
If you look at the step parenting boards, they are full of posters who resent the existance of their stepchildren, or who have little or no relationship with them because the stepchildren resent them, or step children whose other parent (usually the mother although that's indicative of MN rather than society as a whole) has turned them against the step parent. . There are no winners in those situations, only unhappy children.
Overstepping the mark would be the woman insisting your child call her mummy, or putting down her mum in front of her etc. Doing the school run is not overstepping boundaries, it's presumably doing that which her father either can't do because of work commitments or can't be arsed to do. Only you know which. The alternative to that would be her saying "I'm not picking up your child," which wouldn't exactly make the woman a prize catch would it?
And while it's hard to watch your friends become friends with someone who also plays a parenting role in your child's life, it's far more preferable than having a situation where everyone hates and resents everyone else and an atmosphere is caused.
Re the thank you card, I'd imagine that it's just a question of good manners. If she doesn't yet have children of her own then she may think that thank you cards for everything and everyone is the done thing. Why people need to assume that it's a deliberate dig is beyond me. But reality is that life would be so much easier if people didn't try to read motive into everything that someone else does.
Bear in mind that if this woman stays with your ex then she will have a life-long role in your child's life. And while it's very easy to be upset at a relationship between children and step parents when they're little, the reality is that they don't stay children, and one day those children will have adult relationships with you all, and with other people, and the relationships we model to them as children are the relationships they wil want to form as adults. Also, if she has children with your ex then she will be the mother of your daughter's siblings. It serves no good purpose to have a situation where the children have no relationship with the step mother and consequently little relationship with their siblings.
It's likely that you will one day have a partner of your own (assuming you don't already,) and that you will want your DD to have a positive relationship with him and vice versa. And most importantly, that you will want him to want to be a part of her life, and sometimes be prepared to do things for her etc. It's natural to want that. Now imagine how difficult life would seem if her dad started demanding that your partner not be involved in any way... it just doesn't work like that.
FWIW, I have a child who hasn't taken to his dad's new partner at all. I won't go into his reasons here. They're his reasons, some are valid, some aren't, but they've all culminated to bring about a situation where he spends almost no time at his dad's now when previously we had 50/50, and that has been detrimental to the relationship with his dad, and to the relationship with his half brother - the child his dad has with said new partner.
I have spent countless hours persuading him to go to his dad's, talking to him about reasons, wanting to help him through it, and explaining to him that the decisions he makes as a child will have an impact on the relationships he has as an adult. I have stood in my kitchen while he's told his dad that he doesn't want to go on holiday with them because he doesn't want to spend time with his new family and listened to my ex tell him that his concerns weren't valid. FWIW my ex has seemingly come round of late and has said to me that DS does have the right not to like his partner, so I'm not sure what's happened there but something has definitely changed for him. I've gone out and bought Christmas presents for her and her DD on his behalf only for him to be told that he shouldn't mention that I bought the presents (he was at school, I was at the shops, was a no brainer really) because partner would be upset by that. And yet partner, who hasn't spoken to any of us for four years recently sent my DP a FB friend request. 
.
DS is a teenager now and is old enough to make his own decisions, so I've stopped pushing it as long as he communicates with me, and as long as he's polite when there. But life would have been so much easier, especially for DS, if he'd felt at home in both houses, instead of having all this bad feeling in the mix.
And I know that my ex has found it difficult that my DS gets on with my DP. I know that whenever something has happened with his DP he has wanted to know whether DS is the same towards mine, which he isn't. But nobody has gained anything through bitterness and resentment, and DS has maintained his feelings despite what any of the adults think, so as I said upthread, there are no winners.