OP, are you sure this isn’t an attempt to “price” you out of a relationship with your grandchild? As you said, your DIL’s family is well off, they have already bought this stupidly expensive mattress, she knows your family is not well-off, and yet is demanding this. She will point to it and say, “Look, I gave your parents the chance to watch DGC but they just wouldn’t be reasonable, whereas my family didn’t raise an issue at all.” When we all know it’s totally batshit, but if your DS hasn’t stood up to her for 10 years, it doesn’t look good now.
Even if you can work this out somehow, I would pay attention to what @user1471590586 has said. Based on your threads about your DIL, even if this situation is resolved (and I think she’s a cheeky sod - believe me, I know plenty of Forces wives who had to wave goodbye to a husband while holding an infant knowing that NO ONE was coming to help them - I spent a Christmas helping a friend who was too sick to lift her baby because there were no grandparents around to help and she would have given a lot to have a MIL around), you will spend the rest of this relationship with her threatening to cut off contact between you and your DGC every time you don’t do what she says. Unfortunately, DGC will be a constant source of blackmail. You can tell it’s already starting by how she’s framed this.
If she was just a little overwhelmed by hormones and looking at expensive mattresses, that would be one thing. But the fact she IMMEDIATELY framed it as, “If you don’t spend this money, you don’t care for your grandchild,” really shows you how she’s going to run the relationship. It’s going to be, “If you don’t do X, you don’t value grandchild.” “If you don’t do Y, you can’t see grandchild anymore.” Please be very careful about the games she’s starting to play.
Sorry about this, sounds so stressful, and good luck.