Lilibet, this sounds awful, and is an illustration of how intolerant some "Christians" can be.
I'd better put my cards on the table and tell you where I'm coming from...I was brought up a Christian by my C of E parents, attended Sunday Service and other High days willingly through my teenage years and was an active member of "Angsoc" (!) at University. I was terribly hurt by some members of the CU telling me in my first week away from home that I was not a Christian, because I couldn't name the date on which I had been saved- as far as I was concerned I had always been a Christian, and had never come across this kind of attitude. Since leaving University, I moved around a lot for my job, but always made an effort to go to Church and when I settled in one place I boarded with a school friend and her dh who happened to be a priest (C of E). I went to Church regularly then, and when the time came for me to marry a divorce, we were married in church, with the blessing of the Bishop! You may not class me a Christian (and there are other Mumsnetters who don't), but I try my best to follow the teachings of Christ. There are bits of the bible that I don't take as absolute fact, more because I don't understand, than because I don't believe. I don't class that as "picking and choosing"(well I wouldn't, would I?) but as reserving judgement until such time as I have all the info.available.
Enough of me! It seems to me that you have been witnessing by example. It is great that your dp wants to attend Church, great that he is interested enough to discuss it with you, and I bet that, left to his devices and your company he will quietly come to believe. I think the surest way of putting him off would be to ram it down his throat. I have no experience of the Alpha course, so can't comment, But I've heard that it comes on pretty strong....
As for your sleeping arrangements, well, girl, you live in the 21st Century, you are committed and loving, and it is none of her business (was tempted to use some strong language just there).I would have thought it was the job of the minister priest,vicar, whatever to give you advice, not his wife. If he'd asked you to stop sleeping with your dp, I'd still have said the same, mind you, but I think she's completely out of order. I suppose I'll be accused of picking and choosing- I have been before, but I don't see what having a marriage certificate has to do with anything! You have made your commitment to each other, presumably God knows about it, you don't need a public ceremony to say that it is OK to have sex.
What would I do? I would leave that Church, and go to one much more welcoming of couples, married or not. I'm sure your Vicar understands how upset you are, and I would make it clear that I expect an apology from his wife, and reassurance that the subject won't be brought up again.
I haven't been much help, I know, I can't quote chapter and verse to back myself up, but I think this woman, whilst possibly well meaning has behaved in a very unchristian fashion.