my husband refuses to give our child dual citizenship as well. For a few reasons. The main one is if anything were to happen to us, we want her to remain in the UK with his family and not have any of my family get custody of her (long story..sooo not getting into it) .. also because he is proud of being English and doesnt want the US having any say in her life. We have agreed that once she becomes 18, we will support her in any decision she makes in the matter
Potential citizenship and what passport(s) she has probably won't matter when it comes to who might get custody of your child.
If you die leaving no instructions, then social services takes charge. Very unlikely that social services and courts here would give the child up to the US relatives if UK relatives were claiming her. Most likely she'd end up with relatives here because courts anywhere hate to give up anything they have control over. But, once social services are involved, they may always be looking over the UK relatives shoulder.
You are probably assuming that family here would simply 'take her in' without social services ever being involved. That could work out, except it leaves them 'exposed' to potential legal challenges from US relatives because UK relatives can't prove, legally, that you want them to have her. Though again, potentially, if anyone tries to go to court, the system will probably try to preserve the situation the child is in (again, during all that process, she may become a ward of the system.) Even if casually taking her in works out, should something happen to them, worst case scenario of her ending up in foster care could come into play.
Long story short: make a will, name a guardian. Even without citizenship questions, there's too many issues and opportunities for various government agencies to get involved with an orphan and the easiest way around that is by laying out your wishes in advance.
If the thought of a will, or worry over potential costs keep you from dealing with the issue, at the very least, make sure several family members know your wishes. PUT IT IN WRITING, so they have something to take to court if needed.