子供にも分かるような簡単な言い回しで説明して欲しいって英語でなんて言うの？

Could you please use simpler English words that my daughter can understand.
Sometimes can assume that the child can understand but it is good to tell them to use simpler English words so that it is easier for your child to understand what they are saying.
For example: Instead of the saying "The food was delicious." the teacher should say "The food was very nice."
Could you please rephrase that so that my daughter can understand.
If you would like someone to rephrase something it means you would like them to say it in another way without changing the meaning.

When an online teacher first meets, or starts having a conversation with a new student, it is sometimes difficult for them to assess the exact level of the student in the first few minutes. During this period, there may just be an exchange of greetings and normal introductions which are practised a lot. However, of course, later in the lesson, it may become clear the student is a beginner, or their vocabulary is quite limited. As a parent, you may say to your teacher:
"Please would you use just basic words and phrases for my daughter."

"Can you please use simple phrases? She's only a child." Here you can ask the teacher to use phrases that are not complex, and easy to understand. The later half of the response is an explanation as to why it should be broken down.
"Could you dumb it down to a child's level? She does not understand." This is another polite way of asking if the teacher could make it simpler to understand. Dumb it down is a common phrase used to ask someone to the most basic words and phrase for them to understand.

Laymans terms are simplified words which someone who is not a professional can understand easily. The do not require any further study as they are plain and simple to understand.

When teaching children it can be hard as they don't have the knowledge for bigger words as they are younger so you could ask the teacher to use 'simple/easy words' or 'words/phrases my daughter would understand'

"Is it possible to use easy, simple words and phrases during my daughters English lesson?" a very easy an often used way of wording this certain context, simple and used widely by native speakers.
"Could you please simplify the terminology for my daughters lesson in order for her to better understand as she is a beginner"

1.Please work at a slow pace and explain in terms that a
child can understand.
It is best to ask the teacher to work slowly (at a slow pace
which means at a slow speed) in order to allow your child
the opportunity to follow what the teacher is saying.
Terms are words/expressions/phrases/idioms, etc.It is the
abbreviation of the word terminology.

2. Please keep your language simple and straightforward
   for my daughter.
   The word simple is the opposite of complex.It also
   means easy.Straightforward means uncomplicated and
   not difficult to understand.

If you want to ask a tutor/teacher to use simple English so your child can understand, you can say something like "Can you use simple English so my daughter can understand easily please?" or "If possible, can you use basic/simple English so my daughter understand please?".