I have been breeding and showing rabbits for over 30 years, and have owned many breeds, including long-haired ones. I'm sorry to hear you are having this problem. Unfortunately, it's common in pet long-haired rabbits. You were wise not to force the clipper into the coat because a rabbit's skin is indeed fragile. There are not special tools for mat removal in rabbits because the key is to prevent the mats to begin with, but pet stores seldom inform people of how much grooming is involved in rabbits with long hair.By the time a pet owner is aware of it, the coat is a matted mess. I'll give you some ideas in a moment, but often the best solution at this point is to have a rabbit-experienced vet shear off the coat. Don't go with a pet groomer because they aren't used to working with rabbits. If you want to go to a vet, this link will take you to a directory of rabbit vets:http://www.rabbit.org/vets/vets.html
If you want to undertake the project on your own, you'll need some sharp ball tip scissors. You can see what these look like here, and also order if you can't get them locally:http://www.petsupplies.com/item/dubl-duck-straight-ear-nose-shears-4-inch/191514/?srccode=GPPETSUP&gclid=CKmur4SczrYCFa5DMgodVHQABQ
This won't be something you can do in one day because it will be too hard on the rabbit and too tiring for you. Work on it for a little while each day. It may take weeks. First, simply cut off any mats that are not down tot he skin. When you find one that goes too close to the skin, cut into it the long way, making it into two narrower mats, still connected to the rabbit. You may have to do this more than once, but eventually, you should be able to gently tease the pieces of the mat out with a comb.
Once all the mats are out, grooming has to be a daily thing. It's easier if you keep the coat short all the time. A daily brushing, using a comb and/or the ball tip scissors for any mats you encounter, should keep the coat in good condition. If you want to keep the coat long, more extensive brushing and combing will be needed.
Here are two sites where you can read more about grooming long-haired rabbits:https://docs.google.com/vie wer?a=v&q=cache:rvj3MgCao6sJ:www.nationalangorarabbitbreeders.com/tipsforgrooming.pdf+&hl=en&gl=us&pid=bl&srcid=ADGEESgZCY-1hJbjrpnh9rG4IalaJ5eTPFJDsuan-QMePiOlImRdzeNTKiHnzo7QMFfcDIwusnFrxPxEvKm2EhcypBsrGuj6eon2h9pG4p8Jas7-5Qqch8MIMIXw_Gj0kPaudqsxINfM&sig=AHIEtbScRXCTPtpvgwp-2dXU3u3G--1hsw
If you have more questions, let me know by clicking on REPLY. I hope your rabbit will soon have a beautiful coat.