I believe you have to research the Intergalactic Research Network to do what you are asking. Because I can research on two different planets at the same time

I see!

In that case the description of Intergalactic Network is wrong:

Researchers on different planets communicate via this network. Each level allows one extra lab to join with the lab where you begin research, effectively adding their levels together to compute research time.

This would suggest that once you have it, multiple labs can work on a single project together. Instead, it seem to enable individual labs to work on their projects simultaneously.

For reference, I don't have the Network yet and regardless of where I start a research, it gets queued up into a single queue and executed sequentially. And honestly, it doesn't seem to make much sense to me. Why the lab on my colony can't research anything until the lab on Main Planet is finished with its research?

Yeah I see what you mean, but least they have it as a upgrade later.... the research levels are the same on all planets and I believe there is also a cap on the amount of research you can have active think its 3-4 jobs. I only like the upgraded feature because now I don't have to wait for one planet to have the resources I need to research and I can just do it.

The game isn't perfect but its free... the development looks like it has slowed a bit, but so far when I am playing its pretty solid. The game git page is here: https://github.com/steemnova/steemnova

The research inconsistency in 2Moons is a known issue, and unfortunately there is no known fix for it. The best way to avoid this issue is to make sure that all research is completed before moving on to the next research project. Additionally, it is recommended to save your game frequently so that you can revert back to a previous save if needed.