My oldest dd had to wear a patch at 8 y.o. She was VERY resistant to it, but we made it through. Our eye doc said to do active things while wearing the patch, to make the weak eye really work. Reading, writing, and art projects were good. TV didn't count, but using a computer did. I know your child is only 3, so some of this stuff she may not do yet. We didn't watch tv in our house, it was only for movies, so tv was a huge treat. So to start off with, we allowed tons of tv time when my dd first started patching. For the first week or so, we let her watch practically unlimited tv. This eased her into wearing the patch, b/c the first few days or so she couldn't see at all w/the patch on. Everything was blurry and she was really frustrated. So the tv helped get her (and us) over the hump.
My dd needed to patch for 2-3 hrs/day. To do this, we built up to the 2-3 hrs over the course of a couple of weeks. The first few day she only wore it for 5 min at a time a couple of times a day. Then slowly lengthened how long she wore it for. I wouldn't worry about patching the whole time right away. Taking a week or two won't make a difference in getting your dd's eye strengthened, but it will make her happier and more accepting of the patch.
We played a lot of games, and tried to do things where she had to track an object w/her eye when she wore her patch. We'd sit on the floor and roll a ball back and forth to each other. We'd play 2 square (like 4 square but w/2 people). And we have a pinball machine, so my dd would play it a lot. We built stuff w/legos, playdough etc... And she used the computer for games quite a bit. It took a few weeks or more but then wearing the patch became no big deal.
I found some great patches online and let her choose the patterns she liked best. We got two and that was plenty for us. We got them from patch pals (see link below). They fit well on her glasses, and she loved the cute designs. Make sure to get the patch for the good eye!
Oh, and one other thing. It sounds like your dd has to get used to both glasses and a patch. So did my dd. I forgot that we got her used to the glasses first for a couple of weeks before easing into the patching.
http://www.shop.patchingpal.com/cate...5?categoryId=2