しんのすけ is the full first name of the main character Shin-chan, who is their son.
いない means “doesn’t exist”.
So しんのすけのいない means “Shinnosuke doesn’t exist” which is a subordinate clause modifying the following noun, 世界 meaning “world“.
You might wonder why the particle の is used, as が is normally used with the subject in a subordinate clause, which is in this case しんのすけがいない世界.
But in an adjective clause which modifies a noun, の can be used to substitute が. The difference is very subtle but basically が emphasises the subject whereas の emphasises the predicate.
So しんのすけのいない世界 means “a world where Shinnosuke doesn’t exist”.
“Something or someone に未練がある” means “to have an emotional attachment to something or someone” that you used to have and it’s hard to get back anymore but you can’t easily give up on.
So しんのすけのいない世界に未練がある means “to have attachments in a world where Shinnosuke doesn’t exist”.
But in this quote, instead of が, なんて is used to add emphasis and express the speaker’s negative feelings towards the preceding word, which is 未練. So Hiroshi is emphasising the 未練 meaning “lingering affection or attachment” is something disgraceful by using なんて.
Lastly, か is used to make a rhetorical question. When it’s used with an affirmative form, it usually expresses the strong negative declaration. So しんのすけのいない世界に未練なんてあるか means “Do we have attachments in a world where Shinnosuke doesn’t exist? No, we don’t!” or “How can we live without him? It’s impossible!”