2035 a human population on Mars of 500 (mostly workers i.e.: miners, biologists, medical staff, engineers, etc. Most of the colony is underground with above grou lead bunkers. They have an established system of resource acquisition and heavily rely on biotechnology for food and oxygen. Suddenly Earth is cut off, zero communication, zero support. The colony does survive and reaches a population of 859 when colonists from earth arrive in 2090 with the assumption that the colony no longer exists. What sort of culture and resentment would these Martians have towards Earths new global government which emerged out of a World War III.
Earth has entitlement issues.
65 years later, the Martian colony has created a governmental system of their own. Likely, they were under the rule of a terrestrial government before. Now, they rule themselves, and more or less successfully. They've made decisions that saved their people, all without the help of an Earth that is gone.
Their culture is probably very static. Shifts have taken place in areas of production of food and materials, but a colony that size doesn't have a movie industry, or authors, or musicians. Oh, there'll be a few people here and there with hobbies who might produce a little new art, but all of their culture will be based on Earth of 2035.
Now, here come the victors of WWIII. They have changed drastically. They've got a militaristic government, bending all cultures and beliefs of Earth under one government. I guess other cultures could have just been eliminated, but a global government in a post war culture implies subjugation at the least. They show up to create a new colony or to scavenge, and find their lost colony.
"Welcome to the United Earth Empire" "What? No, we lead ourselves" "No, you belonged to us, and now you do again"
This will be the external conflict. They've self governed for 65 years, and now they are just employees again. It's possible that Earth, after war, can't afford to send too many expeditions to Mars, and so rebellion is a possibility. Maybe Mars has discovered a new element or technology that they have a hope of holding off Earth. Maybe the two groups of colonists just assimilate (poorly), and there becomes two castes of people.
Internally, some colonists will welcome their saviors. Others will see invaders. This could be divisive between the older and younger colonists, or between the blue and white collars.
Alternatively, the Earth contingent could set up a separate colony, and trade and conflict happens between the two colonies, with little or no interference from Earth itself. In this case, the new colony would need the "how-to" of survival on Mars, while the old colony might need replacements for long worn out machinery.
Too many unspecified variables, but let's think:
1) 65 years? There should be still alive people who remembered world before WW3. So the cultural drift would not be so far away.
2) There would be still backuped many films, books, games from the old world, so it would be another factor to prevent local culture to drift too far away.
3) That would be clearly enough time to evolve some form of gov, that suits tiny colony. Suiting better well educated people, but simultaneously valuing survival over freedom.
4) There is not enough place for real market economy, so there would be big gov by default. Also any sabotage could be deadly for all, so colonist may accept highly intrusive gov.
5) local people would be used to some kind of semi-authoritarian self govern, and self sufficiency. Those who won WW3 would be treated with nervousnes. There might have interesting technology... but what are their intentions???
If the people knew they could still live on earth they might be very angry.
Thoughts like: "why would they leave us to die?",would be very common, but the second generation of your people should be pretty dumb, they don't have a school and in a world where survival is everything the engineers will only teach things, which the kids can use to survive, also the other people like biologists.
So this generation will not like the earth and their people on it, because they should look like an enemy for them.
I think if they didn't know about the situation on earth they would be happy and would look with hope into a better future, like entering the dream world or if earth is totally destroyed they would be disappointed.
Second thing if they didn't know about the situation on earth they would have build their own culture, they will think we are the best, we cant trust this guys, they are here to use us or something like it.
But in the end I can say the opinions would be very split.