Hello and thanks for your question.
I should start by saying that when parents separate, if they can agree beteeen themselves which parent the children are to live with and how much the other parent is to see the children, then there is no need for any court order.
However, your question implies that your wife will not agree that the children live with her, so that may need to be decided by the court.
In any question concerning children which comes before the family court, the court has to decided the issue on what is best for the children, rather than which parent shouts loudest.The court must take a number of factors into account, set out in the weklfare checklist in the Children's Act 1989. These include the children's emotional, educational and physical needs, the capacity of each parent, the risk of harm to the children from each parent, the wishes and feelings of the children.
In your case, you would be arguing that your wife's alcoholism meant that she could not care properly for the children, and that they were at risk of emotional and physcial harm from her as a a result. If she accepted that she was an alcoholic, then no proof would be needed. If she did not accept that she was an alcoholic, then you would ask the court to direct that she undergo some form of testing, often hair strand testing, to establish the level of alcohol in her body, how it fluctuated in recent months and a liver function test. The test would be carried out by a lab approved by the Ministry of Justice.
However, that on its own may not be enough for you to get a child arrangements order stating tthat the children were to live with you.
In addition, you would need to show how you would look after the children eg by setting out how you currently care for them, given their mother's condition, and how you would avoid disrupting them as much as possible eg by keeping them at the same schools, and - very important - how you would help them to maintain their relationship with their mother, such as what arrangements you would make for them to see their mother (safely) if they lived with you.
For older children, their wishes and feelings will be given a lot of weight by the court, so it will be highly significant whether the 15 years old twins want to live with you, and the court will not force them to if they don't want to. For the younger children, their views do not have such weight - on the other hand, the court is also very reluctant to split children up.
If your wife were to dispute your application to have the children to live with you, it is likely that the court would order Cafcass to prepare a detailed report - speaking to the children's school, GP, making checks with the police and solcial services, speaking to the children themsleves, and then making recommendations to the court - so it would not just be your word against your wife's word, as to which of you the children would be best off with.
If you did want to apply to court, the court form you need is a C100, here:-
However, going to court is stressful, time-consuming and expensive, to be avoided if at all possible. The family court anyway now requires parties to have attempted mediation before it will consider an applciation to court. Here's where to find a local family mediation service:-
I think you would also benefit from some face-to-face legal advice. Here's where to find a specialist family law solicitor:
I hope this helps and I wish you the best of luck.
Thanks and best wishes...