When he was little Harry dreamed over and over of unknown relatives greeting him.
Obviously the 'greeting him' part is wrong. I'm not sure I fully understand 迎えにやってくる.
I'm assuming this is the
masu-stem + に + motion verb
construct, where やってくる is treated as a motion verb. I usually translate やってくる as 'turn up/show up'. So 親戚が自分を迎えにやってくること would be "relatives showing up to greet/meet/welcome him".
Perhaps my real problem is with understanding how to translate 迎える. The English original for this sentence is "relations coming to take him away". But I'm struggling to see how to relate 迎える with 'take away'.