Any advice on how to optimize cellular data abroad?

After contacting customer support of my carrier (Verizon), I tried again all suggestions by the relevant Apple Help pages (also suggested by them), including resetting the network settings, restarting the phone etc. None of this solved the problem permanently, but I found that everytime I switch "Airplane mode" on for a few seconds and then off again, the local Chilean carrier (Moviestar) pops back up with first the letters "3G" next to the 4 bars, and a short while later, "LTE". At that point, cellular internet DOES work - for while, but sooner or later (especially after inactivity but also sometimes while actively using the internet) the letters disappear, the 4 bars remain and cellular data are no longer working. Looks like a bug to me, not sure whose - Apple's, Verizon's or Movistar's.

I'm sorry to say I didn't find a good solution while in Chile (I've since returned to the U.S. where cellular data works on my iPhone without problem). As you can tell, this problem has been experienced by quite a few people. I believe it is a combination between Apple's software/hardware and our specific carrier, Verizon, which seems to only allow Movistar as the local roaming partner (I tried other networks manually and didn't get any bars at all). My friend, who traveled with me in Chile, had no problem with his iPhone - but his carrier is TMobile, which is a more international company right off the start.

In the long term, I will probably switch carriers, as I travel often enough to consider this problem (and Verizon's rather expensive foreign roaming plans) a deal breaker. For now, I recommend to your wife to use the tired trick of turning airplane mode on and back off - it usually helps for a few minutes to a few hours to access the internet via cellular connection.