My wife is worried about my 3-year-old daughter who is not potty-trained yet. She is supposed to start school next month. What should we do?

I have to agree with the comment above. Although I have a similar technique I was able to use for my children. First, girls differ from boys always keep that in mind. So it would be necessary if "Mom" could show her the proper way to pee. Second, before you start potty training her. Buy her a potty chair. Yes that training "arinola" or portable potty you can buy anywhere in the department store. Let her choose what she likes. Third, speak to her with firmness. Remember your goal is to teach her how to potty. So try to remove the soft spot in your heart as much as possible. Explain to her for example " Tomorrow, you will start to potty on your potty chair that we bought. We will practice it together until we get there". If for instance your child shows discouragement or started to whine. Just simply ignore. Believe me she was just testing you if you and your wife will buy into it. Fourth, start the potty. How, just like the comment above, let her wear underwear underneath her clothes instead of diapers. But for me, I let her wear diapers but the potty is right beside her. How do I do it? I time in her liquid intake. If she drinks milk or water, chances are she will pee in 10-15mins after that. Your indication is when she started holding her private part or when she started to scratch it. That's your que. Don't forget the "wiwi"/splashing/whislthing sound like this will encourage her to pee. That particular sound for no reason helps any kid or adult pee without any scientific reason. Lastly, there will be times that accidents will do happen. No scolding! Praise her and encourage her that she was able to pee on her own. Don't forget to still put diapers on at night for the first week of potty training until she was able to control her bladder. My daughter was potty trained at the age of 2 and it only took me 1 day of doing that without any accidents. :)
Magbasa pa