Go to Dancewell. Ask your DD to wear ballet tights (convertible) if at all possible, and clothes that she can do dance moves (at the barre) easily in.
You don't have to make an appointment there, even on the busiest of Saturday mornings, but you might like to ring ahead, just in case they do already know they are astoundingly busy - occasionally they have groups come in from dance schools.
Then sit back, and watch true professionals at work. They have a huge range in stock - DD will usually try on between 8 and 10 pairs, all in her size but from different manufacturers, strengths, marginally different widths etc, all produced like magic from different cubby holes. If by any chance they don't have the perfect shoe in stock, they will order it in and send it, but tbh I have not experienced that.
Expect it to take about an hour (most local parking is on-street meters - buy 2 hours' worth) and expect your DD to be treated absolutely seriously as 'the customer', while you watch. I have the greatest respect for the shop and staff, having seen them at work regularly by now.
They also sell ribbons, elastic, and any padding that you need - essentially they will sell you 'the package' of shoes + padding all together as the padding needed depends on the perfect shoe.
I darn DD's shoes - but I can dressmake and sew well, so I find endless loops of chainstitch faintly soothing. Her teacher won't allow leather tips.