Answer: Such a condition is clearly a sakana that would permit one to carry on Shabbos. However the halacha is that one must do everything possible to minimize the need to be mechalal Shabbos when possible. Therefore, she should not go anywhere that does not have an eiruv on Shabbos, but if she does, she must carry the epipen with her.
Answer: Your son-in-law should ask his Rav if he does not carry because of a concern that the eiruv is not valid l'halacha, in which case your daughter would certainly have to abide by his psak. However, if it is a chumra there is a concept of a man accepting a chumra on himself but not necessarily requiring his wife to follow suit. But I must emphasise that this is a sheila for your son-in-law to ask his Rav.