Translation:I eat between my father and mother.
Because in this case, rather than travelling to some destination or just "being" in a specific location (in which cases you would use "ni"), you are doing something (eating) at a location, so the location serves as context for an action rather than the purpose of an action (so you use "de").
The problem is that kanji usually have multiple pronunciations, depending on the context. If it's a compound word consisting of several kanji, a so-called on'yomi (sound reading) is often used. If the word stands as one kanji on its own (possibly surrounded by kana) it's often kun'yomi (meaning reading). For example: You have the word China. It consists of 2 kanji, 中(middle, inside) and 国(country). Put them together and you'll get on'yomi readings: chuugoku, meaning 'china'. But if you want them on their own to get their seperate meanings, the readings change drastically: 中 on its own becomes 'naka' and 国 becomes 'kuni'. Often kanji have several on'yomi and kun'yomi readings. That's why it would be very tedious and not a lot of fun to many to remember all the readings before leaning the meanings. So it's actually not a bad idea to get used to a meaning of a kanji and get a feel of how it might be read depending on context before actually learning the readings.
Noun と noun の間 means in between the two nouns. However, I would be careful of your understanding of で with verbs.
Location で verb means do the verb at the location. For example: 外で食べる (To eat outside.)
However, noun で verb can also mean to perform the verb by means of the noun. For example, 手で食べる (To eat with ones hands.)
If you look at that, the kanji 間 means a gap or interval. Like in English, it's a concept you can apply to different kinds of things - time, space, relationships (in the sense of between, anyway)
So in this sentence, you have "father and mother's between" - the space between the two people, right? That's where you're eating. I'm not sure if it could imply "eating between Dad's mealtime and Mum's mealtime" if there's already some context (you're talking about when people eat), but with just this sentence alone it pretty much just reads "person A and person B, between them"
(remember の is the possessive particle for something belonging to or connected with another thing. So Xの間 means "the gap/interval etc of X" in a general sense)
I put "I am eating between my parents" and got rejected with the correction of "mum and dad" over "my parents". I thought I remembered putting in "my parents" before and it worked. Either way, would this be an accurate translation, or are you not allowed to make the jump from father and mother to parents?
の for Possession. In English we give direction possession and without possession.
"To my right. To your left." = possession.
" To the left of the building." "I sat between mom and dad= no possession.
In Japanese, the area around an object(s) is possessed by it/them. My left = 私の左
Above the desk? 机の上 (tsukue no ue)." to the left of the desk? 机の左 (tsukue no hidari). To the right of the desk? 机の右 (tsukue no migi). Below/under the desk? 机の下 (tsukue no shita). The 間 Kanji is "aida" in this case for "between, in between, a few other meanings/uses", the space between that belongs to the two things/objects.
父と母の間 = literal: dad and mom's space/in between. Their space in between them
で = particle to mark 父と母の間 as the location where the action takes place.
食べます = eat/will eat
You get used to it over time. I Only made this long in case others had thoughts on direction and such. Sorry.)