Hi,
Good questions here!
Ideally you would give up your greencard at the end of this year, so you wouldn't have to file a return for 2018.
If you're both working, it may be advantageous to file separately, depending on each of your financial and employment situations.
Once you've moved, so long as you can prove than you are permanent residents in the UK, perhaps using utility bills, of if you spend at least 330 days outside the US in the 365 days after you've moved, you can claim the FEIE. You can actually both claim the FEIE for the days in 2017 after you move. Then for 2018, if your wife earns less than just over $100,000 she can claim it if she is still a US citizen or green card holder.
However - if she is paying UK taxes by then at a higher rate than she would owe US taxes, it may be preferable to claim the Foreign Tax Credit rather than the FEIE, giving her a $1 tax credit for every $1 of UK tax she's paid. This could give her excess US tax credits to carry forward.
I suggest you seek some advice from a US expat tax preparation firm. Google it, there are some great online ones who are specialists in this area and also reasonably priced.
Remember though, that US green card holders and citizens still have to file a US tax return from abroad even if they don't owe the US taxes because they are claiming an exemption, and the FEIE isn't applied automatically, but needs claiming on form 2555.
Good luck!