I think $25 is totally reasonable - $20 would be OK as well.
I've learned to value money a little less than people's talents/abilities, their craftsmanship, and skill.
If after 2-3 stitches you were ready to rip up the shirt and the patches - I would say go with your original instinct.
Our society has become so accustomed to the disposable, and 'what I want - when I want it' mentality that quality craftsmanship has fallen by the wayside.
I live in a state where a good deal of people still earn a living by working with their hands, and skilled craftsman are provided a place to showcase their works in a museum quality retail environment. Are their wares expensive? YES some are VERY expensive, can I afford to buy what I would like to have in my own home? NO
However, just because I can't afford something doesn't mean that it isn't worth the price on the tag.
Sorry to get on a soapbox here - but it drives me crazy when people under value the work that others do by hand.
Something I challenge a lot of folks to do is this:
Take your salary BEFORE taxes - and divide it by the number of days a year you are paid - Include paid annual leave days and holidays - AND sick leave.
When you have figured out your gross daily wage (if you are salaried) ask yourself...
Am I worth that amount to my employer? If I were the business owner - would I pay someone that much a day to do my job?
Put things in perspective - value the work of others! Whether it's sewing, cleaning, yard work, landscaping, or anything else physical or skilled labor.
Be fair - you would expect the same if you were on the other end!
$20-$25 is a very fair price - especially since she is doing it so quickly for you and your son!
Once again - sorry to get on my soap box!