I think the key here is your sentence: "bothers me when things aren't done RIGHT with him". there is no right or wrong way to raise kids. There is your way & someone else's way. Anyone who watches your kids will be someone else & therefore, with your mindset, they will do it WRONG. You need to accept that there are other ways to do things. THat said, this babysitter may not be the best (most comfortable) option for you. If you look around you may find someone who matches your personality better. But they will never be perfect & you will always have some issue.
I have 2 kids under the age of 4. Anytime I clean (since they were little) I would leave them in the gated, babyproofed living room & I would clean in other rooms. I was always able to hear them & usually able to see them. My children watch a lot of tv,. I never thought I would be one of those moms, but I am. They love PBS, SPROUT, Disney & Diego (from nick). It is all educational. THey have learned a lot from it. My 3 year old has the vocabulary of an average 5 year old & my 21 month old just started speaking, but he uses phrases instead of individual words. They are both very active. They rarely sit while watching tv. THey are usually standing & running around. If the show tells them to do something, like jump, they do it. THey have learned a LOT from their tv shows. And it has not affected their attention span. THey can both easily watch a 25 minute show, if they like it. (I also take them to the library for toddler story time & they can sit & listen to a whole story, which a lot of other kids can't do). So, what's my point....I don't believe my children have been harmed in anyway by tv. In fact, I think they have learned a LOT from tv. I think the programming she has on is important. If its educational kids shows, then I think its not worth fighting over. IF she has on soap opera's & judge judy all day, then that's worth fighting over. And do your research, not all kids shows are the same. Disney (before noon), PBS & SPROUT are excellent for kids. Most of Nickeloden is garbage (in my opinion, they are entertaining, but don't teach anything real) with the exception of Diego (they learn about animals). I personally, don't think Dora is worthwhile (its like a video game, it does teach about choices, but that's about it).
Well, good luck.