Speaking as a teacher, that does sound to me as though your DD doesn't trust your physical ability to chase after small kids. She doesn't want you to take them anywhere involving potentially dangerous activity.
OP, have you had any mobility problems in recent years? Knee or hip replacements, that sort of thing?
When my DS was born, I would not leave my MIL alone with him, ever. She had not yet had her replacements done, and she couldn't safely carry a baby around. Now he is 5, I trusted her alone with him in her house on our last visit, but I wouldn't let her take him alone out in a busy area, because she would never be able to catch him if he took off (which he does still occasionally do).
MIL is a lovely lady, and if she was 10 years younger it would have never been an issue, but she always understood that DS's safety came first. She had more babysitting with her first grandkids, DS's cousins, as they are much older.
Sometimes it's just how it is. I will probably have the same thing one day when I'm a grandmother. I'll be too old to safely babysit.