My 1-year old chocolate mimosa tree has a couple branches near bottom (not at the bottom of the trunk) that grew alot longer on
the sunny side. Will the other branches catch up, or do I have to cut those off? Don't know how to add a photo
A photo would help, for more specific recommendations. But the general answer is that yes you can reduce the length of those longer lower branches to bring them into shape with the rest of the crown. Cut back to a lateral branch, don't leave a stub. And don't take more than necessary, 10% of the length would be okay, or 20% maximum at one time.