We are on Agnew which has similar houses. Our hall-adjoined neighbours have a young child and occasionally we can hear her in the morning through the hall divide, but never at night. I would assume that you are likely to have the front master bedroom yourself and the children next door are more likely to have one of the back bedrooms. We have never heard a peep until the morning and even then it isn’t at all intrusive. Unless you absolutely cannot stand hearing any noise from next door (in which case detached is the only answer!) I think you'll be fine. If you consider staying in your current house, acoustic underlay can be fitted between the existing wall and plasterboard, it isn’t that expensive for just one room.