But when the child needs to improve, it's totally a different story. I suggest you to send your child to another teacher or coach. It would be a nightmare if you try to be your child's own coach, even if you play chess well.
Let's assume that the parent knows chess well, maybe already a master, is it good for him/her to teach his/her own child? It's a NO.
First, children are not listening to parents, no matter how expert they are. It's much easier for a third party coach to tell the child what to do. It's same as school. Most kids will listen to their teachers, but not their parents.
Second, to make improvement, there will be inevitably a lot of criticisms. It's better to let the professional coach to deliver these criticisms. More efficient and less feeling hurt. The second part is in fact more important. Chess is not our destiny. From playing chess, we want to gain some benefits, no matter it's improving strategic thinking, improving concentration, or enhancing memory and abstract thinking. So we want to keep a close relationship with our child afterward. Acting as a coach in fact is counterproductive.
Third, most parents are not expert in chess. So teaching your child by yourself is like the blind men touching the elephant. It will take you a long time to figure out the correct approach, if you are lucky.
Therefore, seek for help, like in school, in sports, and in any other areas.