Ah op, that all sounds like an awful and devastating shock. No wonder you can't see the wood for the trees.
I think firstly, speak to whoever is in charge of your apprenticeship and explain your situation and see if they can give you some compassionate leave.
Can you do some digging- for him to land this on you out of the blue with no interest in working on it would make me question his motivation to be honest - is it possible he's been looking elsewhere? Check bank statements/ phone records/ everything you can for signs of foul play. If he's been unfaithful and you can find evidence of it then he will pay the fees for your divorce. I'd also look into legal aid entitlement. I called citizens advice and they were able to give me a complete breakdown of everything I would be entitled to financially which was really helpful.
Get yourself a good solicitor and I'd be requesting that you stay in the family home for as long as possible until a financial agreement is in place and you can sell. Then use that money to get yourself something of your own.
I am 6 months post separation and its been brutal. I took 2 weeks off and then went back to work and tbh it was the best thing for me in terms of a distraction.
Seeing kids etc, you don't need to worry about right now - plus you don't know how they'll react to his decision. I would make sure you get yourself counselling and keep it church and state where your kids are concerned. They may be adults but hearing about their parents separation will still be painful so make sure you aren't putting them in the middle in any way.
Then I'd say fill your life with things and people you love. Invest in your friends, invest in your hobbies. I've signed myself up for lots of things I've always wanted to try and honestly, 6 months down the road I don't even miss my stbxh. Things aren't resolved yet but I'm really looking forward to eventually getting my own home which I've a fabulous Pinterest board for and I'm happy enough. In a way I'm glad I'm rid of his grumpy attitude and tip toeing around him which I now know was affair guilt misdirected at me.