Application form advice

I'm in recruitment/HR and would suggest putting 'career break' in the gap on an application form. There's no way you can make this sound good on a form, so it's not worth trying. I am not sure that I would even mention it at interview to be honest.
It's not that you won't get the job based on that, but so many people apply for civil service jobs. Sometimes, if all the applicants are good, employers find silly reasons to not select people as it might be hard to choose someone. It's like buying a house with a crack running through it; a red flag. Employers look for red flags at interview.
I spent time in a psychiatric unit and once mentioned this in an interview for a job in that kind of environment. I could see that it didn't go down well as soon as I said it. It's not fair, but it does happen.

At interview I would say that you took some time out after the breakdown of your marriage, to reassess what you wanted to do and where you wanted to live.

With regards to references, it is a good idea to go with someone who you have known for a while and is ideally in a professional role. For example, I would pick a friend of mine who has known me for 5 years and is a Manager and an ex colleague. You could ask anyone really, but try for someone you know well and is a professional. I have known people get them from their solicitor/doctor/bank manager, that kind of thing.