Messaging failure to non TMobile carrier users.

Hello. My sister, on Verizon, has been having issue's for the past month with her messaging app through her phone as it relates to T-Mobile users. She recently switched to Verizon and set her family up with 4 new iPhone's.
Specifically, the problem is twofold:
1. 1-on-1 text messages: Whenever I (TMobile user) of other TMobile users send her a text message from our phone, she may or may not get the 1st reply, but will never see any response after that. We see her replies throughout.
2. Group MMS messages: Whenever me or another TMobile user is on a group MMS chat that includes my sister, the TMobile users can see and reply to the group chat normally, as can opthers on the chat. My sisters' phone's she has on Verizon does not see anything from either of the TMobile users in the group chat..
She has worked for literally hours with Verizon engineers trying to fix this to no avail. 
Verizon would like TMobile to check my connection to the network and see if they are seeing any issue with my ability to properly send either individual or group text messages. I did not originally think this to be an issue on my end but several other times over the past few months I have sent individuals text messages that were never received to other people outside of my family. There also seems to be a delay in response from when I send the text message to when my phone shows it as sent; this delay could be up to 30 seconds or so, where normally it would be almost immediate.