Verizon sets up MMS service so that it is only available across a mobile data connection, so your wifi shouldn't be playing a role. And SMS service (which is much older technology than MMS and doesn't use the same "mobile data" link as MMS) also uses the cell radio exclusively.
I use the stock messaging app for texts over 160 characters without a problem (it turns them into MMS as the prior respondent mentioned), but I am on MJ7. Don't know if that makes a difference.
I wonder if it is a bug relating to your use of a network extender? You would know if you got a different result when sending texts > 160 chars when you were on VZW's regular network away from your place.
I recently helped my sister out with a similar set of troubles, and the problem turned out that her (at&t) range extender was hung/frozen.
If that was the case, you would have erratic "trouble" sending any MMS messages. In any event, you should see the "network extender icon" in your notification bar - but it might be useful to verify that you do have a data connection through the extender (turn off WiFi and see if you can still browse).
It won't hurt to power cycle the extender, wait for all it's status lights come up correctly, and then see if that changes anything. (You can send yourself text messages).
Hope that helps.
"I'm gonna start coding placebo apps. That way I will be sure that the complaints are real and the praises hollow."