I know this is an issue where many people have very storng points of view, so I will start with mine: I do not think TV is a bad thing as long as it is both in moderation and parents are controlling what is being watched. I think it can turn into a bad thing if it is on too much or the wrong thing is consistently put on. My daughter just turned two at the end of last October and I have given this issue a lot of thought.
With that being said, as long as movies are not on from morning till night, your daughter will be just fine. My daughter loves watching both Dora and Diego. If we are at home all day sometimes she will watch an episode or two, just as yours does though, while playing and going back and forth. There are occasional days where she will watch more than two episodes, but not many. Then there are days where she will watch no TV whatsoever. I noticed soem people commenting on Shrek, I will say that my daughter has seen those movies with me, she just never hung on to them as yours did, so as long as you feel it is appropriate for your daughter, then it is, period! I am a big fan of both Dora and Diego though, they both do seem to teach my daughter a lot of things she wouldn't otherwise know. She can say about 15 spanish words including counting to 6. If you ask her what her favorite animal is she responds with "a pigmy marmosette!" My only advice would be to try to persuade her to go for something that is a bit more educational, Blue's Clues is another good show in my opinion, my daughter is not into that one though.
If you really want the TV off, get some CD's, I have The wiggles CD, the soundtrack to My little mermaid, and a few Cd's full of old nursery rhymes and such that my daughter loves to play!
Tell your mom that she is your kid and while you respect her opinion on the matter, you will do what you want and she doesn't need to criticize. I feel like I've written a book here! Hope something in this rant helps!
A few links not criticizing TV watching, for toddlers over two.
http://www.seattlechildrens.org/home/about_childrens/pres...
http://www.stjohn.org/HealthInfoLib/swArticle.aspx?1,1881
AND JUST TO ADD A COMMENT ON THE ADHD ISSUE:
Kids now are not watching anymore TV than they did years ago, probably less now since our parents were never told it was bad, and the old cartoons are violent! So are we being too quick to put labels on our children such as ADHD now? Because there can't possibly be this many more cases blamed on TV. Anyone feel free to message me on thsi topic if you feel I am wrong, maybe I am missings omething but it doesn't add up to me.