You will be the sponsor. .unlike both going as tourists to visit USA. You are a British citizen, even though you will be visiting you will have to show u can support her stay here.
When the ex mother in law came over we got a family visit Visa.
You state you been living as husband and wife so I would say a visit Visa. When I did the woman's, I got professional advice. .I suggest likewise. Unlike spouse and fiance the visit and tourist visas are a bit grey. Don't trust well meaning hearsay.