My wife and I along with 2 cats, travelled full time for a couple of years so perhaps our experience will help.
First you have two major handicaps we did not have to deal with. Bikes are a major nuisance and you really have to want them to deal with the nuisance. They are not going to fit conveniently in the backseat area. You will need to find a rear or forward carrier that works and fits your needs. Second, a dog is a major handicap, way more so than the bikes. A dog can greatly limit your travels. They are not allowed on trails in most national parks and it is often against regulations to leave a dog unattended in an RV. Even when allowed it rarely works out. With a medium or large dog, you are going to need floor space and perhaps even slides, which I absolutely hate for lots of reasons.
Bikes and dogs aside, I do have some additional comments and recommendations.
We have a Northstar Igloo. I recommend taking a hard look at Northstar. Their campers are well designed and built. For full time and remote camping you will need to add a couple of AGM batteries, solar and a generator. I have 300 AH of battery and 2 135 watt panels plus the Honda 2000. Next, I highly recommend a wet bath. We typically take Navy type showers to conserve water so the splatter is minimal. We use 30 seconds to squeegee 2 walls and the floor and the shower then dries pretty quickly. A wet bath will give you more storage and/or a smaller camper. Next I highly recommend a cassette toilet!! Do a search on this forum and you will quickly see that almost everyone who has one loves them. Dumping any toilet is no fun but a cassette tank can be dumped into an outhouse or flush toilet. With a black tank you need a dump. Those can be hard to find and it is rare that a national forest or BLM campground has one. Even many national park campgrounds do not have them.
