IMHO, yes you are worried with very little cause. In fact I would bring 2 with kids that age. Keep valuables in an easy to grab back pack (Diaperbag). Hopefully you are staying with Disney and can just have purchases sent back to you hotel for you. Otherwise you can have them waiting at the gate for you.
If you cant live with the idea of anything happening to your fave stroller, consider the cost of renting. I highly reccommend that inexpensive on by Graco that comes with a big basket and cup holders.
I use flourescent tape on the handle of mine so i can spot it at a distance. I'd would hazzard to guess its a theft deterant too because it cant be spotted so easily.
If you cant live with the idea of anything happening to your fave stroller, consider the cost of renting. I highly reccommend that inexpensive on by Graco that comes with a big basket and cup holders.
I use flourescent tape on the handle of mine so i can spot it at a distance. I'd would hazzard to guess its a theft deterant too because it cant be spotted so easily.