Hey @ArtUK,
No worries--in fact, sorry it took me a bit to respond to you. I work as an immigration law paralegal and, as you can imagine, it's been a busy period! Hope you're all settled and no longer jet-lagged.
I researched the issue online and it seems your wife can qualify, but it's going to be difficult. All of those documents you listed, such as her travel receipts, photographs of her in the United States, driver's license, bank accounts, tax returns, they're great evidence that she hasn't abandoned her domicile in the United States. If you can include evidence covering the entire period she lived overseas, that would be best. Even better if she owns property, perhaps has a storage unit, or a permanent mailing address in the U.S. Include also the docs Lil bear listed above, such as any future jobs, residence lined up, schools your kids are enrolled in for the future, anything at all that shows your wife is intent on living in the United States. I would also suggest a letter, written and signed by your wife, that explains the reasons why she lived in the UK for so long--family obligations, difficult & slow immigration process, perhaps even some health or family issues, etc.--but that she still considers the United States her primary domicile and she's working on living full-time in the States.
Here are some resources I found about proving her domicile in the U.S., hopefully they will help:
https://www.boundless.com/immigration-resources/prove-domicile-form-i-864/
https://www.immigrationhelp.org/learning-center/proof-of-us-domicile
https://citizenpath.com/proof-of-domicile-i-864/
https://www.novacredit.com/resources/proof-of-domicile
The biggest factor in your case is that your wife has been living in the UK for the past four years, so you'll have to work hard at showing that she never intended to abandon her domicile and the plan was always to come back and live together in the U.S. My recommendation would be to have an extra I-864 ready from one of her family members, just in case; CEAC *sometimes* lets you know why a certain document has been rejected and, if they find issues with the affidavit, you have the opportunity to supplement it. (Plus, the joint sponsor doesn't have to show all the stuff your wife does; they can just show their tax return, passport, and driver's license, with maybe a few paystubs and utility bills if necessary). Be prepared, as the Department of State and USCIS has been particularly strict with affidavit of supports recently.
Hope this helps. Let me know if you have any issues with CEAC!