Need to travel to Europe w/ kids and these phones...

First thing I can think of, do you all need to be online all the time with your phones? Presumably your hotels all have WiFi, as will restaurants, malls, public transport etc

 

If the Verizon devices you've got are all locked, they won't be able to use local carrier prepaid SIMs. So next option might be cheap unlocked devices which can. There's plenty of cheap MVNOs in the EU with good value data packages and international calling rates, like Lebara and Lycamobile. Which I've used when visiting the UK. But to use their SIMs, the phone must be unlocked.

BTW a friend of mine from UK is currently in Seattle for a few weeks, and he's just using WiFi.

 

Call Verizon, I think all of their branded phones are 'world phones' and unlocked. In theory you should be able to get SIM cards, if you can match bands. You need to know what bands/radios are on the phones and what is needed where you're going. The CDMA will be useless but the LTE may be doable.

I quickly checked willmyphonework.net for a Moto Turbo using Netherlands Vodaphone. 2G and 3G will work and 4G (LTE) may:

2G: CdmaOne,850MHz,900MHz,1800MHz,1900MHz
3G: CDMA2000,EVDO,850MHz,900MHz,1900MHz,2100MHz
4G LTE: Band13-700MHz,Band4-AWS,Band3-1800MHz,Band2-1900MHz,Band7-2600MHz" title="" id="device-frequencies" style="box-sizing: border-box;"> Motorola DROID Turbo 2G: 900MHz,1800MHz
3G: 2100MHz
4G LTE: Band20-800MHz,Band3-1800MHz,Band7-2600MHz" title="" id="carrier-frequencies" style="box-sizing: border-box;"> Netherlands Vodafone
2G Network:

3G Network:

4G LTE Network:

900MHz, 1800MHz
2100MHz
Band3-1800MHz, Band7-2600MHz