I may not simply be a matter of size, it may also be a matter of resolution.
In the past, I have tried to send a video which was not able to be sent because it failed to meet the size restrictions of the texting app. I tried repeatedly to shorten the video until it was not worth sending. I then lowered the resolution of the phone when taking another video to a lower resolution and was able to send the video even though the file size was larger then the size of a higher resolution video I had previously tried to send.
I believe I had to lower the resolution to 640x480 in order to send the video attached to a text. Whether or not this is still the case, I do not know as I rarely send video MMS.