Impressive what you are doing under the circumstances.
If you are going to consider children's bikes, a decent one is Islabikes.
Size guide - Islabikes
These would make fine commuter bikes with no toe overlap on the front wheel.
Big brands like Trek offer small sizes, and can be very good, but shops don't want to get one without a purchase commitment. Just as well; you can't trust your own judgment for what is a good fit is anyway. You have no experience at what a good fit feels like. A few millimeters can make a huge difference, and you are off by inches.
So your best bet is to get a professional fit. You should be able to find fitters with good qualifications specific to fitting women somewhere in Southern California. Yes, it will eat a good part of your budget, but not as much as buying the wrong bike. Then become somewhat of an expert on how how to read specifications to find a bike that will work with some part swaps. The fitter should help with that. Then you can order one with little risk.