She can't work because she has to coach our kids.
And.
Now the kids are older they need more attention.
REALLY?
It sounds more like your wife is too scared to work as she hasn't worked in this country as your say.
I'd be amazed if you are allowed to claim UC and she remains unemployed based on the ages of your children alone. The cut off is 5 years old. Your kids are well beyond that. The 16 year old should be more independent than ever. As you haven't mentioned any additional needs I can't understand why she is unable to work?
I know many people with children in your kids age bracket and the majority of comments made are that 'they are at that age where they don't want to be around us', so I can't see why your kids need more attention now they are older?
It honestly sounds like you are hoping that UC will top up your wage and allow your situation to continue. UC doesn't work that way. It isn't designed to keep the unemployed comfortable and off work. Especially without a valid reason for not being able to. The fact you are applying for it shows you know your family cannot live on one wage alone. You cannot depend on handouts. Your wife has to look for work. She is able to work school hours at least.
To be blunt if you are awarded UC, I hope it comes with conditions that she must work or be actively looking for work. My son was only 9 months old when I was told I had to work and I have worked every since. 25 hours, 30 hours, 35 hours and now 30 hours around my sons day. I still have to clean, shop, prepare meals, wash clothes, iron, and do the school run as well as be at school events! As my son gets older he will also need support for exams etc. That does not mean I can choose to not work and support him. I will have to do it as well as work and everything else.
Bottom line your wife needs to work.