I think there's quite a bit of projecting here, the op said that a)there is no schedule, so they'd have to do one just for mil's benefit, as she doesn't seem to accept they don't know where they will be in the time between arriving and leaving. And b)they said they'd have a mobile phone on. They don't have hotels booked, and will probably sleep in the van most of the holiday, so even if she knows where in the USA they are, mil's only way of contacting them would be the mobile phone number. She already has the only thing she would /could use in an emergency situation.
So those of us who have a hard work parent /pil (and it's not mil bashing, a lot of this thread if you read carefully are talking about their own parents, as I am), know this isn't about being concerned, there is no added help to contacting the op from this, it feels like trying to control from a distance.
To me this behaviour feels like a combination of not accepting this is a valid way to go on holiday ("don't be silly, you must have a schedule"- I'd be accused of wasting the holiday or being childish and foolish not to have a typed out schedule and clear plans), and/or making themselves part of the holiday, making this trip planning about them. Op's Mil is worried, mil needs to be contacted and placated, mil's feelings need to be factored into the ops holiday plans. I certainly internalised for a long time that my mums worries where something that had to be factored into everything, so everything becomes about her.
Op, if your DH does insist on writing a schedule, then make a point in the first couple of days of deviating from it.