My daughter is not super spirited and she does play well for long periods on her own (she likes to interact with me, too, but she will read her books or play with her dolls/kitchen stuff/blocks/dollhouse/farm animals on her own.) I did introduce some television and chose specific things for her to watch. She has some 30 minute Noodlebug DVDs, lots of episodes of Mister Rogers that I taped years ago, and I decided that I liked the show Little Bear on Noggin. I did let her watch some Max & Ruby and Franklin (both are Noggin shows) and a couple of PBS shows in the beginning, but I began to feel less comfortable with some of those choices and stuck to Little Bear only.
I did find that it was a great way to get some time to myself, and it saved me when I was needing to fix dinner a few times, and DH would sometimes watch with her in the evenings while I fixed dinner so she did get that kind of interaction. She seemed to be transitioning out of her afternoon nap, which meant she was very needy in the early evening, and we found that letting her watch something then could really help her hold it together. But I also let her watch in the morning, and then I'd end up on the computer upstairs or whatever. So I was feeling less and less comfortable with it. After not letting her watch TV until she turned two, I was suddenly allowing her to watch while I....messed around online to my heart's content. I had started out sitting with her when she watched television, and I'd talk to her about what we were watching, but it was turning out to be more and more of a "babysitting" situation while I was elsewhere, and I wasn't happy with myself.
So I just turned the t.v. off. It worked out that right about when I made that decision, we went on a little vacation with no t.v. She didn't seem to notice its absence, but she asked for it almost immediately when we got back home. But I just decided we weren't going to watch t.v. anymore, or at least not just at her request or when I want to do something on my own, or on a daily basis. I've made no hard and fast rule about it (I haven't made a specific decision on how t.v. will or will not fit into her life), but I don't turn it on anymore. It's back to like it was when she was under two: it's just not on during the day. It's been about 11 days. She asked to watch "a movie" this morning when I went into the living room looking for laundry, but I just told her we didn't have time because we had to go to the farm for fruit and then to the other farm to get our basket of vegetables and some goat milk for her. That got her attention and changed her focus into announcing "I want to go too!" and I didn't hear any more about the television.
I just wasn't comfortable with the way I was parenting her/not parenting her once t.v. came into the equation. I'm also not comfortable with how viewing television might influence her cognitive development, and I decided to be more conservative. I guess I'm holding the issue in abeyance for the moment.
I still think there's value in something like Mister Rogers (though I think much of the value comes in watching with her and being able to reference it later, as shared experience) and I won't rule that out completely for the future. But I think in general, that kind of show (and a show like Little Bear) is appropriate for an older child and so it's not like she's "missing out" while she's a toddler if she doesn't see any more of these shows.
I think I understand where you're coming from (and I don't even have two, or an extremely difficult toddler!) but for me it just wasn't working out. I would have been ashamed to admit how much t.v. she might end up watching in a day, for example. I just felt better shutting it off. I don't know why she hasn't seemed to notice its absence all that much, because she was pretty intense about the television. But I'm thankful that she's been mellow about it thus far!