Of course you're not wrong to want to set ground rules. However, you can only set boundaries for ways in which your ex interacts with you since he has joint custody with you. His time with her is his time and you cannot demand that he spend that time in the way you prefer. You can discuss your concerns but you will only be able to influence him if you find a way to develop a better relationship with him. Your anger is working against you.
As to his girlfriend being involved with your daughter, I see that situation being as more positive than negative. Your daughter is being treated as a part of her dad's family. She is an integral part of his life which does include the girlfriend.
I wonder why the ex isn't paying for after school care on the days she's to be with him. Perhaps you'd feel less annoyance if it was his money he was "wasting." Of course, it would be difficult to set that up now. He'll say he's not using the daycare and thus shouldn't have to pay. Are you sure you can't go to a part time day care plan? It may be cheaper to pay the daily rate if they have one.
He's had this current relationship with his girlfriend for a year. Both he and his daughter had spent time together prior to her moving in. He knew her before reuniting with her a year ago. That is a stable relationship. I don't understand the thought that she's moving too fast. Your daughter has been forming a relation ship with her for months. She had a relationship with her before she moved in.
I urge you to do some soul searching about reasons, apart from your concern for your daughter, that are causing you to feel angry/annoyed. The tone of your post does seem to be expressing more jealousy than concern for your daughter. You didn't describe any way in which having the girl friend involved in your daughter's life has caused problems for your daughter.
You want your ex and his girlfriend to be respectful of your wishes. That is a two way street. Are you respectful of their wishes? It seems to me that the arrangements that they've made are reasonable and not detrimental to your daughter.
Perhaps it would help for you to know that you and the girlfriend are not in competition for your daughter's love. She knows you are her mother and will thrive having a relationship with all three of you. It is in the best interests of your daughter to be on good terms with her father and his girlfriend.
I suggest that you read Non-violent Communication. You can learn a way of talking with your ex and his girlfriend so that all of you are better able to understand each other and your needs and thus be able to get those needs met. They have a web site and a book. Here is a site which describes the philosophy behind it.
http://www.personalgrowthcourses.net/stories/nvc.nonviole...
As to the custody battle, have you considered mediation? I've found that talking together with a skilled communicator can iron out differences.