Hi J.,
One solution might be, to enroll your daughter in Preschool/Daycare!
That way she would not be with them ALL the time and will get exposed to more peer interaction, instead of just the TV all darn day.
Or, you each have your own "time" to eat dinner... just you/hubby/daughter... and at the table, not with the TV.
In our house, (My mom lives with us too), we are pretty loose about dinner "time" and we eat as our habits are. So many times, my Mom, being at her age, she likes to eat dinner EARLY, but we tend to eat later. BUT, I always have dinner made and ready, buffet style... and being individuals we then help ourselves. Our kids eat with US, and sometimes we all eat together. My Mom, likes to watch the TV as she eats too... but with us, we will sit down AT the table, with our kids, and eat. So my kids just are used to the background "noise" but not watching it per say.
As for the baby-talk... well, it seems, from previous postings as well, your girl has good cognition and speaking ability. So, although irritating, the in-laws will not necessarily "stop" though. As she gets older, you can tell your daughter the preferred way to say things... and then that saying "ba-ba" for milk is not a 'big girl' way of saying it. But, each kid is different... and they will not always "copy" the Grandparents and then talk baby-like in return. At least in my kids case, they don't... and they do speak at THEIR own level anyway. And for me, I just explain in a mellow way, the "real" or "proper" way to say things. Because I don't want them to think their Grandma is irritating either. My girl now at her age, 6 yrs., understands and "knows" that Grandma is just old and she has her own ways, but it does not have to be HER ways. So, sometimes I just teach tolerance to my girl (because she gets irritated too),and that Grandma is an "elder" and respect that... BUT, that WE are her parents, or if something bothers her to just come and tell us, nicely.
AND for my Mom, I do explain to her our 'wishes." And in time, we all pretty much have compromised, on both sides, and it has gotten pretty amicable. But it took time...
I don't know how long you have lived with your In-Laws...but, sometimes, habits don't change, especially if they are old. But I know, it really tries our patience...
A funny example: My Mom likes to watch TV too, and the volume is SO SO loud, because she is getting hard to hear. So we tell her we cannot even hear ourselves because it is so loud. So, to compromise, she got TV earphones...so only SHE can hear the TV without causing noise 'pollution' for everyone. BUT, my Mom also tells US "Well the kids are NOISIER than my Tv... and I don't tell them to go away...." And she has a point. My kids ARE loud, especially in the evening.
(so there are 2 ways to look at it). BUT, the TV earphones are a GOOD thing... maybe you can get some for your In'Laws. We got ours from Radio Shack.
All the best, I know each situation is different.. good luck,
Susan