Can't say I'm surprised at the issues with the family not agreeing - if you remember it was something I mentioned quite a while ago - independent people are the best, if they are going to be "out" to their families and their families may not agree - otherwise you are risking the visit from the father with the shotgun.
I'm not surprised at what your partner (and mother of your child, as I understand it) is doing - she has always voiced this opinion to you - sounds like she has tried telling you but doesn't feel that you have listened, so instead she is being open an honest with the folks that you are considering dating.
I think that the two of you should definitely sort out what the two of you want so that you can both get on with your lives, whatever those lives may look like...
"Listen, or your tongue will make you deaf." - Native American Proverb