It's hard to know what's going on in this situation when all we see are a few paragraphs rather than seeing it in person. Are the children feral things or are the grandparents cantankerous old fossils or is the truth somewhere in between? Who knows.
However, I do find it strange that your mother appears to be engaging in a text fight with a child(!) I also find it inappropriate that your parents don't seem to even try to hide their gross favoritism for their step grandchildren.
But we don't need to say who is right or wrong to know it's not working and not good for anyone, as it is.
Your kids might be a bit wild but if the other grandmother likes them, that's a solid vote that they're not over the top obnoxious.
You don't say your parents' ages but I'd caution that sometimes older people don't have the energy they had when they were younger, don't feel well and can be susceptible to mental deterioration as well.
I'd try to keep this as light and calm as possible and just accept that your parents and your children do better apart from each other.
I'd tell your kids they're just old and don't feel well, don't tell them how great they are with your kids' cousins and don't subject them to going where they're not wanted, at least not very much.
Maybe you can keep visits short, or meet in a restaurant with a play area or a park or have your fourteen-year-old babysit while the adults get together.
Maybe when your kids and your parents will enjoy each other's company better when your kids are older.