I have just tried to see what I can find for you, and I must admit that I have not been able to find that much in-depth information. What I have ascertained is that John Donne and Anne More married against her father's wishes, which actually resulted in John Donne being placed in prison initially. However, eventually he became reconciled to his father-in-law and received the dowry that was his due. John Donne and his wife enjoyed a very close marriage, which probably sustained them through the financial difficulties they experienced. In particular, Anne More spent most of her married life pregnant, and had on average one child a year, only dying soon after giving birth to her twelfth child. Donne was grief stricken following this and expressed his love for his wife in the seventeenth Holy Sonnet.
I have included some links for you below that might give you some more information on the character of Anne More and how important she was to her husband. I hope this helps. Good luck!