The biggest thing is that her divorce needs to be final. You are unlikely to get a fiancee visa until you do so. Also, because she has minor children you will need permission of the Father to take the children abroad. Being in a middle of the divorce, are you sure the father is going to be willing to allow this to happen?
Also, you will need to apply for entry clearance for each of the kids as well, as a dependent of someone entering the UK as finacee. The kids passports will need to go, plus the proof you can take them out of the country in the same packet to the NY Consulate, but you will owe 3 visa applications of money.
Proof of accommodation in the UK, your work contract and/or payslips also seem to be missing off the list, as well as her letter. If you are making enough and she doesn't intend to work, then you don't have to worry, but if she intends to work or you suspect you will need financial support from her to be stable, then she will need to include her CV and bank statements.