My daughter-in-law had her 1st baby 4 mnths ago, but she's so clingy with him & won't let me or her own mum help look after him or baby-sit. I'm trying not 2 take it personally, but it's hard.
I'm sure you're desperate to look after your grandson. She's being very overprotective, which can be a sign of post-natal depression, so don't be too hard on her.
Rather than offering to baby-sit so they can go out, why not offer to go over and help out around the house and see your grandson at the same time? Have a word with your son - maybe he hasn't noticed or maybe he could do with someone to listen to him because things at home are stressful. Why not take a different approach and let her know you're there for her whenever she needs you, even if it's just for a cuppa? Hopefully, she's just a little anxious because it's her first baby and she'll soon relax.