Well, first, it’s my understanding (and I’m a musician who regularly attends non-Catholic services in order to play) that you can certainly attend her church, as a visitor, but it does not satisfy your Sunday obligation, so in addition to attending her church, you need to make your obligation. Whether that means attending a Saturday vigil, and then going to her church on Sunday, or going to Mass before or after her services is up to you and whatever Mass/ service schedules are at your particular churches.
In the past, Catholics were discouraged from attending Protestant services, because in the relativistic atmosphere that’s been the case the last hundred plus years, some thought that it “satisfied” the Sunday obligation. And it didn’t help that the Feeneyites, well-intentioned though they may have been, breathed “anathema” to the* idea* of attending a Protestant service, whatever the reason.
But since the 60s, Catholics have been permitted to attend non-Catholic services for good and sufficient reason. With the vast increase in “mixed marriages” in the last 50 years, “good and sufficient” often means that the Catholic partner attends the non-Catholic services and the non-Catholic partner attends the Catholic services. . .at least, that’s the “best case” scenario where both partners exercise their duties in their respective faiths with the full consent and help of their partners.
So, you know you have to make your Sunday obligation. Looks like you won’t have a vigil (it being Christmas on Saturday); but you can almost certainly make Mass and her service, right? If you can’t because the times conflict, you can ask your priest to excuse you from attendance on Sunday with the proviso that you attend a Mass on the weekday before the next Sunday after this one, that Mass fulfilling your Sunday obligation.
Has she regularly attended her church and you yours? It seems this is something new, but surely it didn’t come out of the blue? Has she ever expressed an interest in RCIA? It’s nearly Christmas–buy her a lovely rosary and a booklet on how to pray–and I heartily second jrabs’ advice on the green scapular, too.
God bless you and your dear wife.