We ask Allaah to accept your repentance and to make your repentance sincere.
[al-Baqarah 2:222 – interpretation of the meaning]
With regard to your missing these prayers – in the situation which you mentioned – you did not become a kaafir because of that, in sha Allaah, because this missing the prayers was not a deliberate action on your part, even though what caused it was your drinking intoxicants, which is a great sin, but perhaps Allaah will expiate for it by means of your sincere repentance.
Based on this, then you are still a Muslim, praise be to Allaah. Your marriage is not affected at all and you do not have to renew the marriage contract etc.
After repenting sincerely, you have to pray regularly on time, and beware of neglecting prayers by omitting them or delaying them. Strive to give your husband and children their rights, and turn sincerely to Allaah by giving up sins both major and minor.
We ask Allaah to bless us and our Muslim brothers with guidance and steadfastness, for He is the All-Hearing, Ever-Responsive.
And Allaah knows best.