Hi
Not sure if you were asking this for yourself or as a hypothetical question but my best answer would be that the wife would be in sin if she clearly felt that the Lord was commanding her to be at home with her children to care for and be there covering and she went against what Father had for her, in order to please her husband.The question comes "who is it better to serve, God or man?"
The husband in this case on the other hand is in sin, for a selfish want of spending money he would sacrifice his children care? There is a self issue in the heart of the husband in this case that if he is saved needs to be addressed.
This is only my opinion based on what I have read and studied on the matter. If this is your situation please seek Father and learn what His heart is for you and your family. Pray and keep praying until you know what His will is. I will pray for Father to give you wisdom and to know His heart where your children are concerned and how best to share with your husband about it in a loving Christ like manner.
Sadly I know to many young ones that have fallen into situations that might have been avoided if a parent had been there to be the covering they were appointed to be over their children. To many young ones left to themselves in this world with not enough supervision and Biblical daily guidance. A young friend of mine has recently gone through some things that I found out about(both mom and dad to busy to be involved much) and I think she may be pregnant. Its just so sad. (Please know that I am not saying this is the case with your children just rambling on about things that have been on my heart and your question kind of touched base with things.)
Take care and have a good weekend
EBeth