*I wish we could get an update on this*
Oh and to echo what most people have said, I REALLY think you should dump your boyfriend and spend less time with your sneaky cousin. Because it REALLY seems like you can't trust her or your boyfriend. At all. This is your future happiness at stake. Not family loyalties, not proof of not being crazy at innocent texts(which you know aren't so innocent when they are so frequent)
-wonders how many times people have to say it to you, and how many signs you need to realise what's most likely going on-
*****More stuff adding****
on another note. Your bf and cousin might be texting and stuff. But on phones they might be sending pictures. They could be having *dare I say it* phone sex. Just cos it's over the phone doesn't mean it doesn't count as cheating (I think you said something about they wouldn't have the time or opportunity to cheat, or something like that).
**oh and another thing**
And, I think if you decide to end it with your bf and tell him to move out and stuff, that you should show your mother this thread. Because if she can't understand how you feel about the situation, maybe she'll realise it when she reads everyone else's comments. She should be supporting you and giving you advice, not telling you it's nothing you should worry about.
Oh, and if your cousin has history of bf-stealing, promiscousity, or getting in between people (including your own past, and other family members), then that should be warning signs too.