Would like to know if we can include an AURA component as a child component in LWC component?
No you can not add Aura component inside Lightning web component.
You can compose Aura components from Lightning web components, but not the other way around. To communicate down the hierarchy, parents set properties on children. To decide when and how to nest a Lightning web component in an Aura component, it’s important to understand facets and slots.
No - a LWC can't contain an Aura Component: See here for details
NOTE A Lightning web component can’t contain an Aura component. When you develop a Lightning web component, its DOM subtree must be composed entirely of Lightning web components.
Aura components can contain Lightning web components. But Lightning web components can’t contain Aura components.
Have a look into the standard documentation about Aura Coexistance