Ina is right in what she is explaining, M.. A bifid uvula is a taletell sign of a submucous cleft palate. And yes, it can be genetic. I am wondering if you have a submucous cleft and don't even know it.
Has your daughter been assessed for a cleft? You need to take her to an ENT who will do a nasal endoscopy to look into her structure and see if she has one.
Even if her cleft causes no problems, knowing that it's there is important. One reason is that it can cause permanent problems in speech if the adenoids are removed from a child with a submucous cleft. It can cause a hypernasality of speech because removing the adenoids removes the "roof" of the palate.
My son does not have a bifid uvula. If he did, his submucous cleft would have been diagnosed a lot earlier. Yes, he had severe speech issues (7 years of speech therapy, and would have had more if we had not moved overseas) and yes, he had some real sinus problems (concha bulosa and thickened cilia). I had to fight his ENT about taking out his adenoids because he simply wouldn't listen to my concerns or answer my questions.
You must be your daughter's advocate and search for information so that you can ask the right questions. It's still early to know if her speech will be adversely affected. There are people who have submucous clefts whose speech is just fine. My son was unfortunately, not one of them. In fact, one of his speech therapists never knew until she was in her speech pathologist master's course that she herself has a submucous cleft. They all had to do nasal endoscopies on each other, and that's when they found it. Her speech is normal, BUT, she has never been able to blow up a balloon. Ever. Mystery solved there.
Don't worry about her sticking her finger down her throat right now. Kids without bifid uvulas do that kind of thing. It's not unpleasant to her to vomit at this point. Redirect her as much as you can, giving her something to hold to get her to use her hands to do "something else". If there is a Children's Hospital in your area, get an appointment with their cleft palate team. They should have something like that. It can take many months to get an evaluation with their team. This should include an ENT, plastic surgeon, dentist, social worker, growth specialist, developmental pediatrician, and speech therapist. (Hope I didn't leave someone out.) It's an all day affair, but oh so worth it. They will all assess your child and give recommendations on how to help.
I urge you to remember for later what I said about not allowing anyone to remove your daughter's adenoids. If I had let that doctor do it, I would have deep-sixed my son's already struggling speech.
Good luck,
Dawn