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QUICK ANSWER
"Con quienes" is a form of "con quienes", a phrase which is often translated as "who ... with". "Con que" is a preposition which is often translated as "as long as". Learn more about the difference between "con que" and "con quienes" below.
con que(
kohn
keh
)A preposition is a word that indicates the relationship between a noun and another word (e.g., He ran through the door.).
a. as long as
Me contento con que arregles tu habitación.I am satisfied as long as you tidy up your room.
a. with which
La policía no ha encontrado todavía el arma con que dispararon a la víctima.The police haven't yet found the weapon with which the victim was shot.
con quienes(
kohn
kyeh
-
nehs
)A phrase is a group of words commonly used together (e.g., once upon a time).
a. who ... with
Mis suegros, con quienes me llevo muy bien, me ayudan mucho con los niños.My parents in-law, who I get along very well with, help me a lot with the kids.
c. no direct translation
This refers to an idiomatic word or phrase for which there is no word-for-word translation.
¿Las personas con quienes estabas ayer son tus compañeros de trabajo?Are the people you were with yesterday your coworkers?
Los hombres con quienes me casé eran todos guapos e inteligentes.The men I married were all handsome and smart.