Listen to you bunch of fat old guys. well, I am a 5'7", 170 lbs. fat ass as well.
Glas to hear you are spending quality time with your kid and kudos for the new life.
90 days should be OK but you really have to work hard at it. I am getting back on the bike after a 15 or so years of bike racing and a 10-12 years of no riding at all but eating. for any endurance events, you need base miles. If you can squeeze or get in the simple miles for 2-3 weeks on both the bike or run (I ran x-country in HS to keep in shape for bike racing during off season. That running will last me two life times. Hate it). After that you must ride twice as fast so you can be competitive in the 10 mile event. I would start some type of interval training after that. the distance is short, so you should be able to do it in 90 days. My suggestion id to train for the run and the bike in the same day. They use different muscles. Oh yeah, you will hurt for a couple of weeks. you will sleep well too. If you keep up the the training, you will fly next year. Kids have speed, but we (I like to think) still have endurance. I come to accept that we are no longer Porsches but a diesel truck after my last club with a bunch of hammer heads.
Good luck.
Jeff