Idiomatically I don't think in case of X works very well in OP's specific context. It's usually used in contexts like...
1: He felt like an invalid because he now wore nappies in case of accidents.
...where in case of effectively means as a precautionary / ameliorative measure (either to prevent accidents happening at all, or to limit the bad effects if they do).
It also appears in the standard instructions on fire alarm button behind protective glass...
2: In case of fire break glass
...where in case of means if [there is a] fire. Thus in #1 the specified action (wearing nappies) happens whether or not there's an accident, but in #2 you only break the glass if there's a fire.
To my mind, the connection between these two distinct usages turns on the fact that the specified action is a purposeful response to a [possible] situation (involuntary excretion, fire, whatever). That's my first reason for saying it doesn't work very well in OP's context (there's no purposeful response).
My second reason for not liking it can be illustrated by considering...
3: The doctor prescribed antibiotics in case of infection
...which native speakers will always interpret as meaning the antibiotics are always prescribed (to prevent infection), rather only if the situation (a case of infection) arises (to cure it). To specifically convey that second meaning requires cases to be cast in the plural...
4: The doctor prescribed antibiotics in cases of infection
Thus in principle OP's meaning can be conveyed by...
5: It is more challenging to get adopted in cases of huge cultural difference
...but in practice this is somewhat clumsy phrasing. Plus the connotations of "cases" being "undesirable, but fixable" situations don't really apply here. So I'd prefer...
6: It is more challenging to get adopted if / where there is a huge cultural difference