Well, it's the DM and a US study, if you want to look at the situation in England, then better look at some English research
Having said that there is quite a lot known about the causation / correlation of childhood overweight / obesity:
Parent(s) being overweight / obese (if both are - unsurprisingly - the risk of the child being overweight increases). If I remember correctly there is also an extra link between mum being overweight with daughter becoming overweight;
Lack of physical activity & amount of time in screen based activity (watching TV / playing computer games);
The issue around working mothers rather than working parents is because mums usually take charge of shopping for food and cooking (I know it shouldn't be like that but it is in the majority of households). It's thought not just to be about ready meals rather than cooking from scratch but about mums wanting to maximise positive times and avoid conflict with their children when they are not working, so I understand they are thought to give them more treats (sweets / crisps etc.). Obviously this does not apply to all working mums, my DS was underweight as a teen despite eating us out of house and home.