Okay, let's get started and get as far as we can.
1 - Yes, you can send and receive email with most current Tracfone phones.
2 - @mypixmessages.com is Verizon's mms server -- pictures, graphics, ringtones, etc. (Verizon also has a much older mms server @vzwpix.com) Verzon's text server is @vtext.com. Check it out right now. Send a very simple, very small text msg ('this is a test') to your wife's phone and see if it comes through. You would send it to firstname.lastname@example.org. It should come through right away with no server latency. And since this is your wife's phone, another simple text message that works well is 'I love you.'
Then try the mms server with a very small picture, maybe 4kb or so. This is the same server you would use to send a ringtone to her phone. The email address is email@example.com. Again, very small picture, don't introduce size problems. It should come through with at most a minor delay. mms servers can take longer.
3 - Even though the phone has Verizon parameters (which you can tell by the servers) you may be roaming. Data and mms may not work while roaming. Older phones used to display an R while roaming. See if you can go somewhere with your wife's phone where you know for sure there is no Verizon and see if you get the R or the phone acts strange in other ways.
Try those things and post back here with the results and we'll see if we can figure things out.