I live in SW Arizona and would like to get a new backpack to keep in the trunk of my car. Not really a bug out bag, but more of a "random hiking/camping stuff in case I get stuck somewhere" bag. I can find lots of day bags, but I want one that has a small detachable bag that I can pop off and take on the minor day hikes I do with my kids. My problem is all of the bags I can find with a detachable small bag are the big three day hiking bags, which is more then I need at this point in my life. My google searching has been unhelpful, and thoughts would be appreciated.
I would recommend against a zip-on/off option and instead, take a bag in a bag approach.
I recommend that you look for a small pack made of very light material. Use it as a organizer for your "10 essentials" that you always want to have with you when you're with your kids like 1st aid kit , flash light, fire starter, sun screen... stuff like that. For small mini-walks in parks and other front country or near country venues, you can use the small bag essentially like a dad purse.
When its time to go out on a longer trip, just drop the super lightweight dad purse bag into a larger day pack. That way, you don't have to transfer all the stuff from one bag to another. IME, you should go bigger than you think for your day pack because, as a dad, you'll end up carrying the food, water and jackets.
I have 2 packs that I use for my lighter, organizer dad purse bags. For front-country use, I use a Mountainsmith Daylight Tour lumbar pack. It's discontinued but still available. I find the shoulder bag style (combined with the lumbar waist strap) easier to manage in and out of cars and in buildings and crowded areas. The regular Tour is heavier but worth looking at if you can't find a Daylight Tour.
For backpacking where we hike in, set up camp and then do day trips, I use an EMS packable day pack.
https://www.ems.com/ems-packable-pack/1306595.html
Two that I've tried and rejected... I ran a sling bag for several years. As with messenger bags, I find a single shoulder strap to give me neck pain after a bit. The Mountainsmith Tour solves this. I get the convenience of a shoulder strap for in and out of a car and the comfort of a real weigh bearing hip belt for longer walks.
I also tried a very small climbing pack, the Black Diamond Bullet. I found the shoulder straps too small for big manly shoulders (I'm skinny and they still hurt) so I much prefer the bigger and shaped straps of the EMS bag.