Hi, it seems you're mis-reading. All of Anne's pregnancies were with her husband George of Denmark. You are correct that an out of wedlock pregnancy in her case would have been scandalous beyond conception, but Anne and George were devoted to each other and she was devastated when he died. To quote James Brydges, Duke of Chandos: ‘His death has flung the Queen into an unspeakable grief, She never left him till he was dead, but continued kissing him the moment the breath went out of his body.’

George did contract smallpox along with his daughters in 1697, but he eventually recovered, at least enough to live another 11 years and father more tragedies with Anne. There is a room in Kensington Palace with 18 little chairs and a sign saying "Queen Anne's 18 little hopes" which really makes one visualize the personal tragedy they represent. Her inability to "produce an heir" really pales in comparison to the personal loss involved.