Am I correct in understanding that "Je suis de l'autre côté" could mean both "I am on the other side [and still am]" and "I am from the other side [but am now here]"?
Moreover, there does not seem to be any distinction regarding going to the other side or from the other side. For instance, it seems "Je vais de l'autre côté" can mean either "I go to the other side" or "I go from the other side."
After searching on Google and Linguee, it seems that "à l'autre côté" is not used at all.
Is my above understanding correct? Any verification and additional commentary would be much appreciated. Thank you!
De l'autre côté must be seen as unit/a phrase consisting of a preposition (de) + a noun phrase (l'autre côté). I would call it a syntagme prépositionnel where de does not indicate the origin in space.
You cannot have two prepositions following one another1 and since de l'autre côté is a unit and cannot be broken down, no other preposition is used.
Since in "de l'autre côté" de does not indicate the origin in space the verb on its own carries the position or the direction: je suis/je vais/je viens...de l'autre côté.
This is by far not an exception where aller is not followed by à when followed by a complement of place, it is always the case when the complement of place is introduced by a preposition: aller en haut, aller sur la lune, aller dans les bois, aller sous l'eau...
1Whereas in English this is possible, e.g. "get onto to the other side"
In the context that is considered in the query, "côté" has the particular meaning of surface, space, or part; in the spoken language it takes on often a conventional meaning that depends on the context; for instance, in the context of two contiguous bedrooms "de l'autre côté" may mean "in the other bedroom".
(TLFi) a) [En parlant d'une partie de l'espace située de part ou d'autre d'une ligne concrète ou idéale qui partage un domaine] Partie.
(Quasi-)synonyme direction, espace, région.
1/ No, in a plain literal context, it is not correct;
Je suis de l'autre côté. I am on the other side(This is applicable to the plain literal sense of being, that is, when "to be" applies to position. Of course, when you say that, you don't have to occupy the spot you are talking about.)
ex.: — Tu es dans la rangée de droite en classe ?
— Non, je suis de l'autre côté.
I am from the other side. (This is applicable, for instance to someone's place of belonging if there is a notion of clear division; in French, you would not say "je suis de l'autre côté" to means that you belong there. )
ex.: — Vous avez donc résidé toute votre vie au sud de la Loire …
— Non, je vis de l'autre côté, à Angers. (No, I am from the other side, from Angers.) or — Non, je suis du côté nord de la Loire, je suis d'Angers.
Possibly, there are cases when the "from" rendering is proper, but I know of none.
2/ There is no distinction on one condition: you must add a complement: "de l'autre côté à qqc".
Je vais de l'autre côté quand il fait froid. (This means always that the person goes to the other side)
Je vais de l'autre côté au côté le plus éloigné. (Not the usual context of "two sides". The motion is from this side that is called "other side" to yet another side. However, there is not much of a case for this type of usage because "de l'autre côté" is used almost exclusively to provide an "easy" term for the seconde part of a group of two locations that are next to one another and are similar in some way (livingroom/parlour, shop/storage room, vegetable garden/flower garden, …)
3/ "Vais à l'autre côté", "va à l'autre côté", "vont à l'autre côté", "allé à l'autre côté", "aller à l'autre côté" are not used (ngram); the examples corresponding to "aller à l'autre côté" are false positives. This shows that the verb "aller" is not used with "à l'autre côté".
Do not conclude, however, that "à l'autre côté" is never meaningful, though.
Il faut fixer cette pièce à l'autre côté, pas celui-ci. ("…côté du support de la machine", par exemple; "côté" is more likely to be something line-like in the present example, but in other cases it does not have to be, it can still be a surface or a space.)