If a man says to his wife: If you go out of the front door you are divorced, and his intention was to divorce her, then if she goes out she is divorced, and if this is the third divorce, she is irrevocably divorced from her husband and is not permissible for him until she has been married to another husband in a genuine marriage, not a tahleel marriage [i.e., one that is arranged so that she can then get divorced and become permissible for her first husband again], then he (the second husband) dies or divorces her.
This has been discussed in the answer to question number 82400.
Based on that, this divorce counts as such and your wife is now irrevocably divorced from you.
As for your saying “my wife was the cause, because she is immature and she broke the oath straight away”, you are the one who uttered the word of divorce and made it conditional upon her action, so you are the one who caused the divorce to happen, not your wife.
For this reason a man should control his tongue and refrain from uttering the word of divorce, so that the matter will not get out of hand and lead to him regretting it at a time when regret will be of no benefit and breaking up his family and harming himself and his children.
And Allah knows best.