Chances are, when the time comes for you to pass away, your daughter will be grown up and have her own family. If this unfortunately happens sooner though, the court will take in to account who has been there to raise your daughter and who her legal guardians are/is. Being her legal guardian would take affect straight away, not when/if you die. Your ex is not guaranteed full custody of her should you die. Your ex cannot make you do anything you dont want to do, including having the baby overnight. To make you give her up overnight, he would have to take you to court and have a judge rule it. Does your ex pay any maintenance for your daughter? If he doesnt, then I think he should be providing for your daughter when she is in his care. If he does, he could argue he provides for her therefore, you should provide what she needs when she is with him.
Go and speak to someone at the CAB, they will have the answers you are looking for and will be the best people to advice you on how to go about securing your daughters future with you and your fiance. Dont alienate the dad though as it is best for everyone if you continue to allow him access, even if it is on your terms. Keep thinking of your daughter.