Our research is being ignored by other research groups I am doing a PhD in molecular biology where we conduct research on human skin and skin diseases. Our group (EU based) has been in a discussion with another research group from the USA, where we can factually show that our methods are 'better' and cleaner than theirs. Nevertheless, they keep publishing work where they don't even cite any of our papers. We noticed that our publications were rejected by journals where people from the USA group function as editor/reviewer as well. We are always open for discussion and collaboration because good science cannot be done alone.

Very curious how we should handle this problem.
Continue to publish your results in journals that will accept them.  After a while people will be able to see for themselves whether the US group is ignoring your publications.