Here’s a fun thought experiment from Steven Cox: drop a bunch of colonists who all speak the same language on a planet and let them stew for a few centuries. Come back later and count how many languages they now speak. What can we expect?
Well, in general I’d say these are the things that tend to make languages diverge:
1) time
2) high population
3) lack of writing or recorded language (writing makes language more conservative)
4) lack of communication between communities
5) contact with speakers of other languages (not a problem in your scenario)
6) a sense of community identity
7) a poor relationship with their cousins across the border
So your settlers land on a planet and and all of their kids speak English (or whatever). The settlement grows until it’s about 200 people (Dunbar’s number) at which point it fissions and some families leave to start their own settlement.
Now you have two settlements. They swap people and information, but within a generation, speak with recognizably different accents. This process continues until you have a dialect continuum, with people in a given settlement able to understand everyone in neighboring settlements, but unable to understand people at three or four degrees of remove.
Transportation and information technology (books, airplanes, phones, the internet) will slow this process down, but unless these people have teleporters, geography will still play a role. Children talk most with the people who live in their home towns, and it’s when you’re a child that you develop your personal language.
Politics will play a role, too. If one language community closes its borders to the people and media from another community (like North and South Korea) differences will mount up faster. On the other hand, a wealthy, powerful, influential speech community will erase differences as people imitate it (like American English from the 1950s to the 1990s).
A good real-world example of this sort of linguistic evolution might be Spanish-speaking Latin America. They all speak Spanish, but it’s been 500 years and there are significant dialectical differences between different speech communities, which haven’t always been at peace with each other.
Assume in about the same time frame our space colonists will be a little bit more linguistically homogeneous than Latin America (because of technology and a lack of any substrate languages like Nahuatl or Quechua influencing things).