Bad breath or "Halitosis" in children can occur due to several reasons like poor oral hygiene, mouth breathing, tooth decay, gum disease, infections in the mouth, bacteria on the tongue, dry mouth, tonsil stones, foreign objects in the nose and some medical conditions.
Start with improving the child's oral hygiene by ensuring she brushes twice a day and making sure she brush the tongue as well. Take the child to see a dentist to exclude oral infections, decay, gum disease etc. If it's still persistent you may need to see a paediatrician as well to exclude other causes'.

I don't think so. Most Public clinics don't open actively during weekends

I gave birth at Gbagada Hospital Hospital and it wasn't bad. My friend gave birth at Island Maternity Hospital and it wasn't bad too. Both Government Hospitals are some of the most used by mothers in Lagos State