The rats go where they can get water food and shelter. So take 2 of them away. Make sure all food is sealed, no crumbs on surfaces, wash dishes directly after eating etc etc. Make sure there are no wet pipes under sinks, toilet seats are down and few puddles etc are outside your house if it rains.
To get rid of the ones you have, you should use snap traps instead of poison because of your young family. If the only food in the house is on snap traps hidden under furniture etc the rats will find it because they have excelent smell. (there is no need to put them in the open).
I'm a rat keeper. I keep them as pets and they are adorable.
But wild rats around the house is no good. They will chew wires and could set your house on fire. Go and buy a dozen snap traps, keep them baited and you will have no problem.
You have a family of rats, and they have marked your house (usually by sneezing droplets on walls etc) so they will keep coming back. The little buggers would sneeze on me if I let them out of the cage, I watch them toddle off and they often return to where they sneezed in increments and fan out a little further at a time. Its how the plot the landscape, and gives them an anchor point.
Basically they are coming from your neighbors. They will be eating the rotties dogfood. You need to tell your neighbor he needs to feed the dogs at specific times, rather than leave dry dogfood in bowls 24 hours etc. Feed them, then when they are done, seal the rest of the food until next time.