
This is the right time to address anterior crossbite. Annabelle currently has mixed (primary and permanent) dentition. As her permanent teeth come in, this is the ideal time to intercept spacing/malalignment issues because of the leeway space due to the difference in size between the primary and permanent tooth that comes in. Normally primary teeth are slightly spaced, so Annabelle’s slightly crowded teeth should be monitored by an orthodontist (which is what you are doing).
Good reference on leeway space : http://orthonj.com/leeway.html
Children are remarkably adaptable, so I think that it’s likely that Annabelle may in part be slightly posturing her jaw forward slightly so that her teeth fit together, i.e. a functional anterior crossbite, although a dental exam would be needed to determine this with greater certainty. With the anterior crossbite, her teeth can only bite together a certain way – correct the crossbite and her upper to lower jaw relation will likely spontaneously improve. It is also possible that a “protruding lower jaw” may indicate a skeletal discrepancy. To keep this discussion basic, let’s assume that Annabelle’s crossbite is her only issue.
In general, there are different approaches an orthodontist can take to address a problem and it depends on what they feel most comfortable doing. She is recommending either: (a) fixed appliance (i.e. the limited braces option); (b) removable appliance, which are the two broad categories.
The terminology you mentioned is not technically correct – a “retainer” serves to keep everything in the proper place (root word retain), not to move teeth into the desired position. Although many dentists may (Your thought is correct about wearing a retainer following orthodontic treatment for the rest of the patient’s life, or for a good number of years at least). So the proper term in this situation is not “retainer”, rather “removable appliance”.
The textbook solution to a simple anterior crossbite is a finger spring removable appliance with posterior bite plane. Other possible approaches include a similar appliance with a screw instead of a finger spring, or an inclined bite plane alone.
The orthodontist might be recommending the fixed appliance option because she can do it “in-house”, i.e. it costs her only her own time and a few materials, whereas the removable appliance needs to be sent to a dental lab and so there will be a lab fee involved (the cost of which is usually passed along to the patient). But a simple finger spring appliance is not expensive, I would guess maybe $175 to 200.
Maybe the orthodontist has other factors in mind that I don’t know about. Otherwise, considering just this information, I would go with a removable appliance because Annabelle can take it out to brush and floss her teeth. She’s a good kid, so I would think that she is reasonably responsible to not lose it. Braces would make dental care more difficult and increases Annabelle’s risk of cavities. Annabelle is a little young to be trying to take care of her teeth in braces, so this route could be challenging.
I would recommend looking around and getting a free consult from another orthodontist and see if you like what they say and what prices they quote you.
Another suggestion: until Annabelle starts her treatment, you can ask her to put finger pressure on her bottom tooth that sticks out whenever she thinks about it. Orthodontic movement is best achieved by light continuous force.

Image (above) of appliances from: https://www.dentistrytoday.com/orthodontics/1563–sp-133686282
Image (below) of lower inclined bite plane with before and after pics from: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3169927/pdf/DENTISTRY2011-298931.pdf
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