Hello Cary, I am not familiar with this story but from the context here 'blown up' means to be killed/destroyed in an explosion. 'Land up with' is similar in meaning to 'end up with'. So Harry's mother was killed and this is how Aunt Petunia came to look after Harry. Hope this helps Bob

In this case "got landed with you" means that Harry needed to live with his aunt and uncle and they did not want him.

It means she has been killed in an explosion. The expression "got landed with you," means that the person speaking feels that they are stuck with the person to whom they are speaking - it means that the person that is being spoken to has replaced the person that was killed in the explosion and that the person doing the speaking does not approve of the replacement!