A combination of what FC Mommy and Boss Fan said: Tell them this is about liability and that if they do not pay in full, immediately, she must be removed immediately because your liability coverage will not cover someone who is not fully registered (and she is not). Combine that with Boss Fan's idea of a mandatory meeting with the parents--telling them that if they do not attend in person, their daughter is off the team. (Yes you might have to not tell either parent that the other is scheduled to come.) At the meeting, that's when you hit them with the liability issue and the request for immediate payment. Have that in a letter you present to them there, in person; don't go with only verbal communications. Make clear to them that you have allowed her to practice out of concern for her and that she is very upset about having to sit out at times due to their nonpayment, but now things are at a point where their nonpayment is jeopardizing the entire team's ability to keep practicing and attend events.
If they do the "it's his turn to pay/it's her turn to pay" argument, just cut them off cold and say, "I am not involved in or interested in your personal arrangements regarding who pays. There must be a payment made before you leave here today and it does not matter which of you makes it. If neither of you is willing to pay today, your daughter is off the team effective the moment you walk out the door without paying. I am devastated to do this to a great kid like your daughter but the issue is not her -- it is the lack of payment."
C., I really feel for you and for this kid. You are trying so very hard to help her out when this is not her fault. While others are saying the parents are gaming the system so they don't have to pay, I think that it's much likelier that they are just using the girl as a pawn; mom throws everything onto dad, dad throws it all onto mom, and then each can blame the other when daughter is upset, and they both get off on blaming each other. I would have a hard time being as tough as some folks are saying you should be, and I understand why you have been so easy on this girl.
It might take the meeting above or possibly a registered letter from an attorney to shake them up.
Alternatively if they refuse to meet, tell the friend who does the pickups that you cannot let the girl into the facility at all due to the fact her fees are unpaid. Do NOT say it in front of the poor kid, though. I'd ask to speak to the friend alone for a moment and inform her that you have consulted your attorney and your liability insurance means you no longer can have an unpaid kid inside the facility though you were allowing her to sit in previously. When the friend hauls the girl home that might give the parents a wake-up call that you are not going to provide free babysitting for their child.
This is all so sad. Please update us here.