Howdy,
I may not be your favourite person right now but (in my previous post) I really was thinking about the flowergirl experience from your daughter's point of view.
Anyway, you should not rely upon an informal arrangement with your ex-husband in this situation. Even if he complies with your wishes for the time being it is useful to have something that will have the force of having consequences. This is not a personal attack on him and if he really doesn't intend to violate your wishes then he will have no problem with you proceeding.
First, you mentioned that you have "joint custody." I hope that this is a formal order that is contained in your dissolution of marriage final order and not just an informal arrangement between you two. What you should do is contact the judge that issued the final order and that handled your case. You can write him or her a letter including your case number and a copy of your order and request that the order be modified. You can visit the court clerk who can answer your questions on how to get the order modified.
what you will be seeking to do is to attach some conditions to the arrangement and since you are not seeking to actually reduce your ex's visitation, make it supervised or increase his responsibilites, adding the additional conditions of him not allowing contact with certain third-parities (your sister) during his visitations should not be a problem for the court--especially since he (I assume) doesn't have any familial bonds with the third-parties you are seeking to exclude.
Naturally, you must be prepared to explain to the court's satisfaction why you are seeking to exclude THESE particular third-parties and to place this RESTRICTION upon your Ex. This is not an easy hurdle to get over but you should have enough evidence, including your testimony as to why that contact is 1) detrimental to your daughter itself and 2) detrimental to the relationship between you and your daughter--mostly because of the impact upon your daughter's perception of YOU by the situation (shunning) and any disparagement (verbal) of you that may occur during such contact.
As a third factor you could argue that while your ex (having his own parental rights) has some legitimate claim to how he desires to influence your daughter's religious and spiritual development, these third parties do not have such standing. Because there is already going to be some conflict created by your influence versus your ex's, to allow additional third parties who are specifically going to create ADDITIONAL conflict will only serve to increase your daughter's confusion and development to her detriment. This is especially true until your daughter reaches an age and level of sophistication where she is better able to sort through such different viewpoints and begin to draw her own conclusions and make religious and spiritual decisions for herself.
I would concentrate on points 2 and 3 above. Point 1 will get you into a quagmire that the court will not want to get into as it will require an analysis of JW doctrine and culture and exactly why those things themselves are directly detrimental to your daughter.
Arguments 2 and 3 are much easier to prove and deal specifically with the practicality of the situation and most judges are for the most part pragmatists.
[I saw a ridiculous post about the child molestation issue. It is ridiculous because it is HIGHLY unlikely that your child is actually endangered and to drag the issue in is unreasonable. However, the issue is germaine in the sense that you can use the issue to your advantage by bringing up with the court, should the procedures get this far, such relevant concerns that attending meetings (unsupervised by someone other than of your designation--perhaps your ex) and participating in field service (under similar conditions) may expose yourself to an UNKNOWN (undocumented-unprosecuted-unconvicted) sex offender due to specific Watchtower policies and ecclesiatical (judicial committee) procedures that make it possible for such a person to have association with your daughter unknown and unsupervised by either yourself or your authorized designee. Naturally, you will require some actual testimony and evidence to this point but if things were to get this far such evidence may be very pursuasive.
However, this is with regard to meeting attendance and field service and I am unsure if these are issues with you or not. It seems to me that you are seeking to go much further than this and forbid even non-physical contact between your daughter and her aunt including telephonic, electronic, and even postal communication so these factors regarding the Child Molestation issue are not truly relevant to these non-physical forms of contact.]
Much of this whole process you can handle yourself without the aid of an attorney and if you are nice to the court staff and get them to help you.
I hope the above practical advice will help you. By the way since I am an attorney in California and you are not in CA, I have to give my little disclaimer that the above is not intended to be legal advice in your jurisdiction and you are further advised to seek counsel in your own jurisdiction.
having said all of that, I disagree with you that you should seek to cut off all contact with your family on behalf of your daughter. you are the one DF'd not her. She should be entitled to decide for herself whether she would like any contact with her aunt and grandparents.
When she is older and can understand more THEN you can arm her with as much of the facts (but not the negative baggage) regarding why you feel she should not have contact with your Aunt.
--Eduardo