I don't think that anyone is accusing you of lying @notjustaprettyface just simply being unreasonable and having unfair expectations. You immediately jumped to blaming DIL when perhaps your son prefers spending time with her family also. You getting into conflict with him and placing blame on the woman he loves most in the world before anyone else will not create harmony, it will only create divide. You are going to end up losing access to your grandchild and, not because anyone is using your grandchild as a weapon (when I hear that, it always makes me roll my eyes) but because they will see your behaviour as emotionally immature, emotionally manipulative and toxic and they won't want that influence around their child.
Your best course of action would be to reach out and apologise, tell them that you're just upset because you miss them which has made you lash out. Reach out to DIL, take accountability for your behaviour and tell her that you would like to try to build a closer relationship with her at HER pace. You're never going to have a close relationship with your grandchild if you can't treat DIL with love and respect.
As for DIL spending more time with her family, yes that's normal - things don't have to be equal. These are people's lives we are talking about, this isn't a football match where you should be keeping score. Just be grateful for what you do get and appreciate that time.