Dogs and apartments, lots of potential for issues to arise. Few are unsolvable. We know nothing about the issues surround this particular situation but having had many dogs of my own for over 30 years and working professionally with owner training for over 10, I'm approachable if this family would like some advice in giving the situation one final try. A move can be stressful for pets.
Dogs need attention more so in an apartment where they cannot amuse themselves chasing bugs and lizards in the yard all day. Dogs need to get some exercise to release energy and their bowels 4 times a day, every six hours is not unreasonable and anyone who has "had to go" and can't knows how uncomfortable that can be. Few people relish the idea of getting out of bed and heading out for a walk before the coffee is ready. Dog owners need to have the tools and skills to do basic maintenance like clipping toe nails so the clicking on the floors doesn't drive them nuts. Most importantly, patience. Dogs are pack animals and want to please provided they understand their place in the pack and unwanted behaviors are curtailed and good behaviors reinforced continually. The dog is 100% dependent on its people and they are usually the source of many of the issues.
In the end, a dog in an apartment requires the same amount of work but requires more time and effort that can really limit one's freedom to be away from the home for extended periods of time. If the people are able and committed to meeting the needs of the animal, it should be possible for everyone to reach a happy place. If one's lifestyle does not allow for the time and consistent attention to the needs of a pet, then re-homing is the best option for all involved. It is much better to come to this conclusion sooner rather than later. A dog is like having a perpetual two year old child. They will always set the agenda, need things that sometimes cost money, and curtail any notion that you can leave for the beach at noon and not come home until 10pm without finding a puddle and a pile on the floor. When circumstances change, sometimes, people just can't meet the needs of the animal any longer, unfortunate but reality nonetheless. I wish this family luck in either resolving the issues or finding a good home where their beloved pet can thrive.