I can share with you what I know from my own experience with my animals, from working in a holistic vet clinic and working as an animal consultant.
First, it is a good idea to have a cardiologist determine what is happening, if you can afford to. A sonogram is very expensive, but gives full description of condition your dog is in.
Based on the outcome, or an intuitive one you can either put animal on meds from vet or go the holistic route or both. I prefer holistic and minimal meds, so I work with homeopath who is well versed in allopathic too. Homeopathy saved my cat's life two years ago, after he was on heart medication and aspirin which almost killed him. I have a thorough description of what happened to him here: http://nourishingkitty.wordpress.com/tag/homeopathy/
on my cat blog, and how my homeopathic vet literally saved his life with Naja, a Cobra snake remedy.
The short verision is: when a cobra bites you, your heart fills up with fluid, and your lungs collapse or fill up, so the homeopathic remedy addresses those very issues. I know of a holistic/homeopathic vet in Santa Fe who works over the phone if you want/need a referral.
Additionally, if by abnormal rhythms you mean cardio-myopathy, CoQ10 is amazing for this condition. My other cat, Rosie, has been taking since she was a kitten for a congenital heart condition, along with CardioVascular herbal Formula from Rx for Pets. Also the Naja got rid of my other cat's cardio-myopathy completely.
I hope this helps, and let me know if I can help further.
All the best,
FYI~Fish oil is imperative to breaking up clots in the blood.