It might be a good idea to really brush up on social media and learn how businesses are using it. There are very few companies these days not using some form of social media and if you have a good working knowledge of it from a business standpoint you might be more competitive. It also might help you find new job leads.
I understand you are the primary caretaker to your children but if you need computer time to look for work then you must establish that daily.
I'd imagine your W has some obligation/requirement to inform you where she will be taking the children and "her new apartment" is not sufficient. Has she disclosed where she will be living exactly?