Translation:My father is next to my mother.
The part about tonari is still true, but I've looked it up online and apparently, yoko can be used for any two entities that are right next to each other, including people. So yoko can be used as well as tonari in this context. I would say: do google this one for a bit more context and nuance!
According to http://yesjapan.com/YJ6/question/4683/soba-_tonari-_yoko_what_039-s_the_differen yoko can be used for any two things that are physically right next to each other (even if they are the same type). となり means that two objects of a given quality are one after another, but it doesn't mean they have to be physically touching. So for example two towns might be となり even though they're twelve miles apart with a hill and a forest in between, because there are no other towns in between (just like in English we would say "the next town over").
This word means that an object is located on the sideways direction of other object. Unlike 隣 (tonari) which concern which requires the same type of categories, the object you’re describing with 横 (yoko) doesn’t have to be the same type/size/category. As long as the object is located in either left / right direction of something (horizontally)."
It needs to be "My father" and "My mother" because you are using the terms for father and mother that you say when talking to other people about your parents. However, "My father is beside my mother" is correct. Yoko means beside (or at the side of). Tonari means next to.
It is accepted in written exercises.
Unfortunately, it is currently impossible for us to add any alternate answers for listening exercises. If the main translation doesn't contain the kanji, the listening exercise won't accept it. We recommend you use tiles for listening exercises when possible in order to help circumvent this issue, but we do hope there will be a fix for it some day.
Not really no, 父(ちち) is a very friendly and close word; it really just refers to your own dad. お父さん(おとうさん) is a more formal word, you can use it to refer to your own father as well as any other father in the world.
So this sentence would specifically mean "(my) dad is next to (my) mom."
"My father is next to my mother" is 「父は母の横にいます」while "I am next to my father and mother" is 「父と母の横にいます」(you could also say 「私は父と母に横にいます」but the 私は is not needed).
The difference is the subject. Since in the first sentence 父 is marked with the は particle, it's the subject, but in the second sentence 父 is connected to 母 with と which means that they are both connected to 横にいます as objects; the subject of the second sentence is only implied.
Kanji: 父＝ちち 母＝はは 横＝よこ 私＝わたし