If you can ping the inside interface of the router then your config is OK, certainly I can't see anything glaringly wrong with it.
Check that the default gateway on all your internal machines points back to 10.10.10.1, or at the very least they have a route to the 10.12.12.0 network pointing to 10.10.10.1.
If that's OK then it may be a switching bug in the router code. Try enabling "ip cef" on the router. If that doesn't work try turning off fast switching with "no iproute-cache" under the dialer interface. there was a lot of old bugs with fast switching but they should all be ironed out long ago, but they do seem to crop up every now and then and they do have these symptoms.
