Google "ua5799" and you'll see that this morning's flight arrived at terminal 2, gate E6. Flight 1769 departed from terminal 1, gate C25. It's a long walk from one to the other. The
Detroit-O'Hare flight was on an Embraer 175, a midsize regional jet. Are you sure the agent said you could bring the chair into the passenger cabin? They're normally gate-checked and brought up from the hold to the gate at the arriving airport. My son rides a wheelchair. He can walk onto and off the plane but can't stand for more than a few minutes. Our practice is to wait for most of the passengers to disembark before getting off. This makes getting off easier and allows the ground crew time to bring the chair up to the jetbridge. I wouldn't try to get off ahead of other passengers because the chair is still making its way up.
You can get wheelchair assistance through the airport. Whether that ends up being faster than going on your own depends on whether the assistant shows up on time and how fast you and your daughter can go.
I think you have a decent chance of making your connection but you shouldn't be surprised if you don't. If that happens, United will rebook you on the next available flight. Their next nonstop to Santa Ana leaves at 4:09 PM. Today's flight has six seats available, but no seats together. While someone might be willing to move to let you and your daughter sit together, you can't count on that.