First...If there are bears in the park and there may not be any, they will be out anytime of day. The camp staff usually know if there are bears in the park.
The reason you do not take your dog on a trail is because they usually will run off and find the bear. Then, P**s the bear off. The dog runs back to you with a bear on his tail. If you need to take your dog with you on the trail make sure he is on a leash.
If a bear wants in your trailer, dog or not he will get in. Keep your site bear safe and you will not have any issues. Talk to the park staff and they will give you their thoughts on what to do about your dog.
Don't be afraid of bears so that it wrecks your holiday...but be respectful of where you are.