Rely is different from count on. If you rely on someone than you have little to no choice but counting on someone means you "trust" that person or its actions. Let's say you rely on your brother as he has the money and you don't. If you count on your brother to give you money, than it just means that you believe and trust that he will give some to you, but it does not mean you don't have your own.
"Rely on" should be accepted.
I think it's not the same meaning.
Contar con alguien = Count on someone.
"contar" can also mean "to have"
ex: La casa cuenta con dos dormitorios y un baño./ Las cases cuentan en sus puertas un señal. I guess that "nosotros contamos en ella con...something, mean "we see.(something) in her." = "we see her as..." Maybe not this exact meaning, I don't know.
I found occurences of "contar en" on the Internet:
[La unidad de cuidados] Contamos en ella con equipos médicos para atender casos como arrestos cardiacos, = the care unit has teams of doctors, etc...
La primera lección es sencilla. ¿Qué te contamos en ella? Pues cosas muy prácticas.= The first lesson is simple. What does it contain?
[La naranja] sus proprietas se deben a su composición química. Contamos en ella vitaminas B1, B2, C, etc = It contains vitamins B1, B2, etc..
There are 4 possibilities for translating "you" from English into Spanish: Ud. (singular, formal), Uds. (plural, formal), tú (informal, singular), and vosotros (plural, informal, used in Spain but not much in the Americas). Oh, and I guess there's vos but that's only used in certain countries (I think it's singular and informal).
Going from the Spanish to English, it is what it is and it's all "you" in English.
I think you mean la cuenta. La cuenta is the check or the bill, like in a restaurant. El cuento is a story. It's super easy to mix up. But these are the nouns. The verb is contar. The verb by itself can loosely mean to count or to tell, depending on what context it's used in. It may help to think of it as when people say, for example "there was an account of a mysterious noise" or "he accounted for his whereabouts", to help you remember that it also means 'to tell'. It's a little fancy or old-fashioned but maybe it helps.
Just definitely don't ask your waiter for el cuento unless you want him to sit down at your table and tell you a story. In that case, go for it.
It is kind of annoying that ustedes is always translated as "you" first with so many language learning softwares, i have only heard people say "you all" or "you guys" at least in the USA and if you just said "you" to a group of people here they would be confused and wonder which you are talking about. At least that is my experience.