Entered triathlon. Had bad bike accident and concussion. Wife doesn’t want me to try again. Training without problems. What should I do?

Be careful. As long as all concussive symptoms are gone you should be fine but the more concussions, the more risk for long term issues.
See MD, talk to wife. Clearly you must resolve this with your wife. You should also be cleared medically. Which is more important -- health and healthy marriage or completing triathlon? You be the judge. Maybe you both could help with the race and see where it goes from there. She may understand it better and your desire to do it, and you will have paused to reflect on priorities and helped your fellow triathletes.