"I'll order, mom."
Translation:E ʻoka au e māmā.
Technically you have a good point. But in Hawaiian, this sentence is a command form. If one says e oka ana au, then the better interpretation might be something like "I will be ordering." The first person command form e oka au translates more closely to this prompt given in English.
The command form in Hawaiian implies an immediate action when taken in first person, whereas e [verb] ana implies an action further into the future. For example, e hele au implies "I am going right now." But e hele ana au implies "I will be going (when time is appropriate to go). Clear as mud, I suppose.
For this prompt, the action seems immediate, like when ordering food in line at a restaurant, so e [verb] au is the more appropriate choice. But in the same breath, you are not wrong.