Welcome, and I hope you are able to find a path that is right for you. Obviously I don't know your wife and kids

so take my advice for what it's worth, but my strong personal opinion is that your spouse is someone that you really want to talk to about this sort of major change in your life. I started my journey to my current status by telling her, and she was very surprised and still says she doesn't really understand why I wanted to be castrated but she was OK with it on the grounds that it was "My body, My choice" Because of our respective medical issues sex was already not an option, but we can and do still 'cuddle' and otherwise enjoy each others company, so you should be able to tell your wife that losing your balls does not mean you can't love her in other ways... Almost all of the members here that have been castrated and want them still have active love lives
Whether or not to tell your kids is more of an open question, it probably depends a lot on how close to them you still are, as to whether or not you feel they have a "need to know".
I did not have a lot of problem with getting the psych letters or really any of the medical stuff once I was able to convince myself to go to the Transgender center near where I live, which is what I suggest for most living in the US. However I have no idea how such things work in your country, which has a very different culture and system.
Good luck
WheelyFixed
Paraplegic - T-5, ASIA-B. 2010 Injury left non-functional & frustrated. 4/24/22, stop T. 5/4 start 3.75mg Lupron. 6/29 - T ~0. 7/7 - start E. 9/2 stop Lupron. 3/30/23 - GOT LETTERS! surgery (O&S) 9/28/23. Doing 0.75mg/day E patch as HRT