El Raval has a rough reputation which dissuades most families from living there. It's also known as a 'young' or, more cynically, as a 'seedy' area due to the many bars that can be found there.
Where in El Raval is the apartment? The closer to the docks the apartment is, the rougher the area feels.
Generally, though, Barcelona is quite safe. If you're happy renting in a lively, area with skateboarders and the odd drunk, then the lower rent might be worth it. It's also a fairly central area.
Otherwise, you might find it useful to read this Expat Arrivals page on areas and suburbs in Barcelona.
Hope this helps.
Thanks for getting back to me Kyle. Your reply definitely confirmed some suspicions I had about the area. My family and I are now looking for accommodation elsewhere. After reading the link you shared with me, I see that areas like Pedralbes or Sarria are more suited to our needs. Thank you for clearing this up.