HATE my daughters name

Emmalee

I'm seriously considering asking my husband if we can change my daughters middle name. shortly after we decided to name her after my mil, it came out that she was having an affair with our 22 year old family friend. after that I really didn't want to give my daughter her name. I waited until the last minute to fill out the birth cert. because I just didn't want to put her name down. she's caused a lot of pain to the whole family and has been using "the kids" to hurt my fil. telling him things like the kids wish you would die, knowing that he has had suicidal thoughts. we were all keeping it very private, since that's how is family opperates. they were supposedly going to work things out. but now she's constantly posting things about this kid on social media and people are starting to ask questions. I'm so embarrased to tell people my daughters full name. and to top it all off, she had the nerve to bring this person to my older daughters birthday party instead of coming with my fil....it's just all so disgusting me. does anyone know how difficult the process is to change a name?