Spending on immature children is responsibility of father, and if a husband (father of children) does not provide money for their expense, then the wife can take required amount from his wealth without seeking his permission.
حدیث: عن عائشة، ان هند بنت عتبة، قالت:" يا رسول الله، إن ابا سفيان رجل شحيح وليس يعطيني ما يكفيني وولدي إلا ما اخذت منه وهو لا يعلم، فقال: خذي ما يكفيك وولدك بالمعروف".
Translation: It has been narrated from Ayesha (RA) that Hind daughter of Utbah said: O Messenger of ALLAH! Abu Sufian (her husband) is miser and do not give me as much as should be sufficient for me and my children. But yes (it is enough), when I take from his wealth without his knowledge. Prophet Muhammad (Peace Be Upon Him) (ﷺ) replied: “As per the customs/ traditions you can take as much as would be sufficient for you and your children.
(صحیح البخاری، كِتَاب النَّفَقَاتِ، بَابُ إِذَا لَمْ يُنْفِقِ الرَّجُلُ فَلِلْمَرْأَةِ أَنْ تَأْخُذَ بِغَيْرِ عِلْمِهِ مَا يَكْفِيهَا وَوَلَدَهَا بِالْمَعْرُوفِ:حدیث نمبر:5364)
Spending on children is rewarded and has been emphasized number of times in Ahadees and the good news of reward on it has also been narrated.
عن ابي هريرة، قال: امر النبي صلى الله عليه وسلم بالصدقة، فقال رجل: يا رسول الله، عندي دينار، فقال:" تصدق به على نفسك"،
قال: عندي آخر، قال:" تصدق به على ولدك"، قال: عندي آخر، قال:" تصدق به على زوجتك، او قال: زوجك"، قال: عندي آخر،
قال:" تصدق به على خادمك"، قال: عندي آخر، قال:" انت ابصر".
Translation: Abu Hurairah (RA) narrates that when Holy Prophet (PBUH) (ﷺ) gave instruction of charity, a man said: O Messenger of Allah! I have One Dinar (Gold Coin). Prophet (PBUH) (ﷺ) said :” Use it for yourself”. He said: I have one more. Prophet (PBUH) (ﷺ) said: “Give it to your son”. He said: I have one more. Prophet (PBUH) (ﷺ) said: “Give it to your wife”. He said: I have one more. Prophet (PBUH) (ﷺ) said: “Give it to your servant”. He said: I have one more. Prophet (PBUH) (ﷺ) said: “Now you know better (whom to give)”.
(Sunan Abi Daud: Hadith Number: 1691)

If the father does not spend, where should the children go?
حدثنا ابو صالح، قال: حدثني ابو هريرة رضي الله عنه، قال: قال النبي صلى الله عليه وسلم:" افضل الصدقة ما ترك غنى، واليد
العليا خير من اليد السفلى، وابدا بمن تعول". تقول المراة: إما ان تطعمني وإما ان تطلقني، ويقول العبد: اطعمني واستعملني،
ويقول الابن: اطعمني إلى من تدعني، فقالوا: يا ابا هريرة، سمعت هذا من رسول الله صلى الله عليه وسلم، قال: لا، هذا من .كيس ابي هريرة
Translation: It has been narrated by Abu Hurairah (RA) that Prophet (PBUH) (ﷺ) said: “The best charity is that which is given when one is rich, and a giving hand is better than a taking one, and you should start first to support your dependents. A wife can say, "You should either provide me with food or divorce me." A slave can say, "Give me food and enjoy my services." A son can say, "Give me food; to whom are you leaving me?" The people said, "O Abu Huraira! Did you hear that from Allah's Messenger (ﷺ) (last part of Hadees)? " He said, "No, it is from my own understanding."
(Sahih Bukhari: Hadees Number 5355)
While these Ahadees give knowledge about the virtues of spending on children, they also clarify that not spending on them is a sin.