Placitas, New Mexico
Although I know that many people would be excited to know that they are sharing their land with rattlesnakes, I don't get the feeling that a "congratulations" is appropriate in this case. I've written a lot about living near venomous reptiles and the associated problems and, unfortunately, there are no easy solutions. It is possible to relocate rattlesnakes, doing so doesn't necessarily mean a death sentence for the animal, but catching venomous snakes increases your chance of a bite. It is possible to kill any and all rattlesnakes you encounter, but again, most venomous snake bites happen when people try to kill or harass these animals. It's not a good strategy for you or, of course, the snake.
So, there are a couple potential strategies for dealing with the individual rattlesnakes that you may encounter around your home, but none get at the root issue. That is, you're living in rattlesnake habitat. If you find one snake, that likely means there are many more present because it is unlikely that you happened across some rogue traveler. So, to answer the first question, whether the presence of one snake means there are likely more around: yes.
The few snakes that we do observe are a small fraction of the number of snakes actually out there. In a way, that's good news: it means that we probably overestimate the risk we have of a dangerous encounter with a snake. We're close to snakes every day with no problem. That said, one bad incident with a venomous snake is too many. The best long-term strategy is to make your yard and home inhospitable for snakes so they have no reason to stay. That means removing any hiding spots and getting rid of anything else snakes might be attracted to, like rodents. I created a brochure on the topic that is available here.
Many species of rattlesnakes den communally, that is, many individual rattlesnakes spend the winter together underground in burrows or rock shelters. Rattlesnakes do not lay eggs, they give birth to live young, so they do not have nests. However, the rattlesnakes often give birth in the fall around their dens and shelters so there may be a congregation of animals in one spot (for more on the interactions between mothers and offspring in these areas, check out Melissa Amarello's blog).
Rattlesnake litters can be anywhere in the neighborhood of 5-25 animals, depending on the species and the individual animal. And, if there are a few mother rattlesnakes giving birth in the same spot, you can see that the number of rattlesnakes can get quite high (although many of the babies will be eaten by other animals).
Can snakes get in through a dog door? Unfortunately, there's no reason to think they could not. Anyone that has had a snake as a pet knows that these animals have an exceptional ability to escape their cages by squeezing through tight spots and pushing off lids. And, anyone that has encountered a ratsnake in their attic knows that they can penetrate even seemingly secure strongholds. Having a swinging door at ground level is just making it too easy for snakes and is not advisable when sharing the land with rattlesnakes.
As I've written here, I think the best solution for your dogs is aversion training. But I haven't heard from many people regarding how well it works. Readers, please offer your tips for sharing land with rattlesnakes, particularly if you have dogs.