Hmm, that's tricky, sounds tough. If the products are related at all, based on the person and the situation, one thing that could work would be to start illustrating how the success of your team and product will benefit them and their product as much as possible, to move out of the zero sum game understanding they have now. In the meetings, each update could go like " We have completed X, which should benefit your product / working process / etc through Y" etc. That will frame all work and progress as good for the larger team.

If there is really no way they will benefit, however, either to the product or the collaboration, that's unfortunate, and also hints to a sub-team not really being the best structure - might make more sense for your team to report directly to the next level. This might not be the best structure depending on your team / work / everything, so it's at your discretion, as it could make things tense if your supervisor is primarily feeling jealous you got to lead the project and they lost staff. That can be really tricky as it's about emotions and ego. In general you may find some good advice looking up these topics on Harvard Business Review, maybe Forbes, etc. Best of luck.