I agree with the others. Especially that this sounds like a relationship and control issue more than a parasite issue. Kind of reminds me of this weekend. An out of state dog hating relative who we rarely see came over. The dog jumps on the bed and goes to sleep. "You shouldn't let the dogs on the furniture!!" (this dog is only allowed on the bed, not the couches..)And it wasn't just about the dog, she comes in like she owns the place. She doesn't knock on doors, just barges in, helps herself to anything in the cupboards, fridge, bathroom.. anything she wants. If she can't find something she *needs*, she'll look through everything. Completely rude. I seriously think out of state relatives can be controlling because it's their lame attempt at being part of your life and they don't know what else to do or how else to act.
Did you ever think about how this situation would be any different if this was your child instead of your dog that most people think are so easy to get rid of? With parents like this, you would have the same problems you're facing now. They'd tell you how to raise it, they'd disagree with some of your parenting skills, as it got older they'd be telling you who to let him/her date instead of telling you who you should date. I'd guess if you ever decided or happened to become a single mother, you'd run into even more problems especially with your father being a minister. They don't even understand that your dog is your "baby", How would they act if it really was a baby? If you adopted a baby that they were convinced it also had "parasites", would they recommend you get rid of it too?
This is NOT about the dog here! You get rid of the dog, and it will be something else they'll be on you for. You said your relationship with your boyfriend is going nowhere..whatever that means. Seems like you've been with him a while since your dog is old now and you've raised her since she was a puppy. (after all those years how can you even consider getting rid of her now? :(
But if you break up with him and get a new boyfriend, how long before the new boyfriend has "parasites" or something wrong and you have to get rid of him too? Seriously, really think this through. Post in some relationship forums, ask a therapist..etc.
What is wrong with the dog anyway that you're so convinced she has parasites and needs cleansing? What breed is she? Please post some of her symptoms and maybe we could help you with that. Poor diet and health in general can cause problems that have parasite symptoms in people like scratching, bloating, constipation, gas, dry skin, smell, lazyness, etc. Whatever you *think* is wrong with her could be some common problem we all have heard about it. She might just need a diet change, not parasite cleansing.