Yes, it should be possible for humans to occupy two planets peacefully. If humans can occupy two continents, two countries or two states peacefully, there shouldn't be any difference extending the distance to two planets. In fact, I think that this may actually help to cut down on social discord.
Though there would be peace for some time, the exact amount I do not know. Earth and what ever planet or planetoid we colonize, be it the moon, mars or venues would eventually find them selves at odds with one another which could lead to war. Much like what happened between England and her colonies in north America, when king George III raised taxes. Conflict is bond to erupt, be it over taxes, resources or to simply declare independence and let’s not forget boarder disputes can cause wars too. Lets say mars, Venus or the moon have acquired independence and separated themselves from earths governments to create their own. Who knows what could spark a war then, but one would be bond to happen given time.
Humans are failing miserably at inhabiting our current planet peacefully. People are discriminated against on a daily basis based on race, gender, religion, sexual preference, etc. Occupying another planet would only provide another means to segregate the human race. Before thinking about occupying an additional planet, we need to concentrate on finding ways to peacefully inhabit the one we're currently living on.
I don't think it's right for humans to colonize other planets. There are enough issues on Earth that need our attention and treatment. If we don't address those issues properly, those struggles will only extend to other territories that we command, no matter where in the universe those territories may be.
Hypothetically explaining to a child (or a space-alien with no understanding of our culture) why something is the way it is is just a good way to get a person to assess their own opinion or make them realize they're just following unsourced traditions or emotional responses.
It's where you go to bust up an argument made solely on enthusiasm, visceral disgust, or always-been-this-way illogic.