It depends on the severity of the cavities. If they have progressed past the initial stages, they will need a filling. If not, there is potential for reversing them with good mouth hygiene. Your dentist will be able to give you the best indication of how far along your children's cavities has progressed to. If you're not happy with one dentist's assessment, feel free to see another one.
The first step to take is to encourage your children to brush their teeth regularly with toothpaste that contains fluoride. When doing this, they need to ensure they don't swallow the toothpaste as regular consumption of fluoridated toothpaste can increase the risk of fluorosis (healthysparx.com/questions/11606/ ...). Your child's dentist should be able to pick out a good toothpaste for your child's needs.
Certain foods are more likely to cause tooth decay and cavities than others. In particular, any foods that contain milk, ice-cream, honey, sugar and sugary drinks (including soda), raisins, dried fruit, cakes and biscuits, candy, chips and dry cereal are more likely to cause tooth decay. Instead of all these sweet foods encourage your children to eat fresh fruit that has lots of fibre and water that encourages the foods to be easily washed away from the teeth by saliva.