V.L.
My son is turning 10 next month; and has too many issues to list besides Autism. For children with texture issues, try a big bottle of Johnson's baby lotion (the big pink bottle), with the push down squirter. This has been a great "calming" tool for us, besides putting him in the shower.
My son also had to have a pair of socks on his hands for about two years because of the sensitivity. The lotion is what helped us move away from that. Without the lotion, he would hit his head repeatedly until he bruised himself so bad it looked like he was being abused.
A package of balloons works well. Don't blow them up real tight, they need to be "squishable".
Also, these children love music. My son will listen to Josh Groban or Andrea Bocelli; but the key is to make sure the REPEAT button is on for the player. We have listened to the same Barney and Bear in the Big Blue house now, repeated over and over - back to back now, for the last 10 years. And since he only sleeps for 3 hours (in a 24 hour period) you know how exhausted and sick we are of hearing it.
Lastly, since she is 4, and you want to be outside, by a very small blowup kiddie pool that she can sit and lay in, while someone sits outside with her. Make sure the water is warm (let is be in the hot sun for a while). When the warm water is on there body, but they can feel the breeze also, it really soothes them.