My questions is quite similar to Mysqldump from the Amazon RDS. I have the same behavior. Everytime when I do a backup using mysqldump my entire RDS freezes and hence my application is not responding. I am using --single-transaction with the mysqldump command but that doesn't help at all. With this, RDS is quite unusable since I can not dump a backup or data sample during live operation. Is there a way to get the data out of RDS without freezing everything?
I suggest taking a look at processlist while the DB is dumping. There could be locked MyISAM tables causing queue of statements waiting for locks to be released.