"My kids want to adopt a cat and dog."
Translation:Mes enfants veulent adopter un chat et un chien.
You're totally right. This is one more of those -sadly to much frequent cases- where Duolingo unnecessarily bows to some local usage not to say bad English.
Sometimes it's to mirror the French structure but in this case it's really absolutely unnecessary.
And it damages the English of many non-native English-speaking users while stirring insecurity in others about “how should I say that in French!”.
This is an example of ellipsis, a perfectly ordinary syntactic process used more freely in English than French wherein repeated words in otherwise parallel clauses can be dropped, which can include articles if the two things are thematically linked: "I'm eating with a knife and fork" "He's bringing a cake and bottle of wine"
But not if they're totally unrelated: x "My children want a dog and television"
I know the feeling - so many rules, so little memory! AFAIK, at its simplest, the subjunctive is required in a subordinate clause when certain conditions are met in the whole sentence, including the main clause. One of these conditions is that there is a change of subject, which isn't the case here - it's mes enfants all through, hence the infinitive adopter in the 'subordinate' part. If the English sentence had been I want my kids to adopt a cat and dog, the French would treat it more like I want that my kids adopt a cat and a dog and the subjunctive is required just for the adopt part. See https://duome.eu/tips/en/zz - use the drop down Table of Contents to get to "subjunctive"