Grandma is Ma's (adopted) ma. She believed her daughter had run away, but she always held out hope that she was still alive. During the seven years Ma was gone, Grandma turned Ma's room into a gym, divorced, and remarried. She's happy Ma is back, but it's not like they can just pick up where they left off. When Ma ODs, Grandma takes care of Jack. It's frustrating for her, but she finds a good balance between letting Jack be himself and teaching him the way the world works.
Some of the lessons Grandma teaches Jack are part of growing up, like when she won't bathe with him naked the way Ma does. But some of the lessons are a little more difficult, in a "this is the way the world works, but we really wish it wasn't so" kind of way. Like when Jack hugs a boy he just met on the playground and Grandma tells him "we save our hugs for people we love" (5.575), the implication being that you can't love someone you just met. But the world needs more love, the kind of love Jack has to give.
Grandma is perhaps being a little over-vigilant in this case. Jack has a habit of being very trusting of strangers, and he does almost go off with two women at the mall at one point, but what's the harm of hugging a kid on the playground? The lesson here is that it's hard to give love when we live in a world of fear, but Grandma is doing the best she can.
Jack ends up getting along well with Grandma and the new man in her life—Leo, his step-grandpa, whom he calls Steppa. Steppa is pretty laid back. He's glad he never had kids, but he gets along well with Jack. Steppa is happy to let Jack get angry, hit things, and yell… and then just move on with life. Jack bonds with Steppa, but we don't see Ma do the same thing. The nicest thing she has to say about him is, "He's nearly seventy and stinks of dope" (4.989). But we don't think she gives him enough credit. He's a lot more supportive of her, and of Jack, than her own father is. Maybe when she sees how well he and Jack get along, she'll open up to him as well.