T., I don't think you can deal with your daughter sleeping in her own bed until you and your husband are in agreement. As you said this is affecting your marriage also. I recommend that you tend to the marriage first. If I were you I would go to counseling. If your husband won't go with you, you go. Even alone you can learn skills that will help you deal with your husband.
Does your husband back you in other issues? If not, I think that you will have difficulties with boundaries and discipline throughout your daughter's life if you don't find a way for you and your husband to willingly agree on this issue.
I suspect that the co-sleeping is a relationship issue, not just a family issue, for your husband. Teasing his brother about co-sleeping (I think you mean that his brother did co-sleep) and then wanting to co-sleep when you don't doesn't make sense. It sounds immature. Or perhaps he's working out some issue of his own that involves excluding you. By teasing he was also excluding his brother. It seems the result is that he and your daughter are together and you're the odd man out. I certainly would not move out of the bed.
For a short term solution you could set up a sleeping area (a mat on the floor) for your daughter in your bedroom. That is one step removed. And then quietly move the mat closer and closer to the door and on into her room. But I suspect your husband will catch on and the battle will be on again or it won't ever stop.
It is imperative that the two of you agree on this issue. You are right that your daughter senses the tension between you and it is affecting her total life and will have a negative result even when she is grown. Especially since it involves the parents' bed. Although she is consciously unaware of sex now, that situation will have sexual overtones for her when she is
older.
This may be more information than you want or even need. But I think it may help your husband understand why it's so important to get your daughter used to being in her own bed. This is a Freudian theory and many other psychological theories do not ascribe to the oedipal stage of child development. It occurs between the ages of 3 and 5, and is when the child is attracted most to the parent of the opposite sex and may be angry with the parent of the same sex. There can be competition between the mother and child for the father's attention. The child will feel most secure when the father doesn't play into this behavior. This changes around the age of 6 when the child once more represses their sexual feelings. I studied this years ago and didn't do much research right now but I have seen little girls flirting with their father and believe, as do the experts, that this is good as long as the father puts out definate boundaries.
Fights, disagreements all negatively affect the children but I think that this one is worse. If you cannot reach an agreement then I'd let her sleep with the two of you for now. Your daughter needs this sense of security.
And start some counseling! I think that the real issue is issues in your marriage.
I know this is an especially difficult issue and time for you. I wish you the best as you work it out.