I haven't read all the replies, so I do apologize if there is some repetition here.
First off, coloring in books at our house would be the first issue I'd address. You've said your dd knows not to do this but has difficulty controlling that impulse. I'd do one or both of these: Put all crayons/markers out of reach and/or put all books out of reach. I'd explain that we do NOT scribble on books and that I was putting things up until she was older and able to act respectfully.
Do you have a dry erase board? They are pretty cheap and you can buy one with magnets that attaches to your fridge. Very good investment. Also, if you want to leave art supplies out, what about putting easel paper on a large portion of your wall and having crayons underneath for coloring. We do this and it works well and saves on books of blank art paper. Chalkboards are also good since they are eraseable.
If you're going through 50 books a week, and you buy all of these books, then you should have a fairly large collection. I'm not the parent of your child but my child has an amazing memory and I would say that after 100-200 books, she would have forgotten the first set of books we read. When dd was about 2.5 she went through a novelty phase, but we had a large collection of children's books so we just rotated often. Beginning at age 3, I started reading less books to dd. We read one book with breakfast, one with lunch, maybe one with dinner, and 2 at bedtime. I try to get books that are seasonally appropriate or have some connection with our lives (like a pp mentioned). This makes them more fulfilling. We have a set of about 10 books per week that I rotate when reading, and the next week, I have a new set of 10. I like having set reading times because I believe that at age 3 a child needs to be doing many other things besides reading--not that reading is bad, but there are so many other things to explore. What about choosing 10 books per week and then after each, acting out the story or painting a picture about the story, or something creative to draw out the experience and make it more in-depth.
Do you have a used bookstore near you? We buy most of our books at Half Priced Books or ebay. Chapter books are great for this age, especially ones like Winnie the Pooh in which each "chapter" is a story in and of itself. I would visit a good used bookstore and get several story collections. They aren't hard to find and cost about $5 each for 100 or more stories. Also, www.mainlesson.com
has some really great stories for free online. Can you make up your own stories together to tell or write down in book form (just fold paper and staple)?
Things like zoo memberships and museum memberships aren't really necessary at this age but just fun. If money is tight, just forgo these and get some good nature books from a used bookshop (National Geographic has a great children's set that I found at our used bookstore for $2 a piece). You could also take out a nature magazine subscription, like Your Big Backyard from the National Wildlife Federation. At a used bookshop you can get a fun science book with experiments to take the place of a children's museum, or just browse online preschool blogs. There are some really good things online. I've gotten great ideas from: http://www.perpetualpreschool.com/sensoryideas.html
. Ask on the homeschooling board for good blog recommendations. Montessori blogs are really fun usually. Little Acorn Learning is also a good resource, and online you can get two free samples. We currently do Seasons of Joy, and that has lots of game/crafting/story ideas, and is only $15 per season.
To me, it sounds like your child is actually bored with reading. Maybe she is just enjoying "mama time" while reading but is not really enjoying the experience so much and doesn't know how to express it. I would definitely focus on doing other quality things together. My advice is to read less and play more. For when you do read, buy story collections or chapter books or get free stories online. Do things at home that are free: Go on nature walks (perhaps take a plant field guide), paint together, craft together (my dd loves cutting craft store felt while I make felt playmats for her), bake together, plant seeds. There is so many wonderful free things in this world--free concerts, free zoo days, free air, free snow. We recently had fun making our own ice skating rink in a pie plate for dd's plastic animals. Life doesn't have to be so expensive. It just sounds like you need some fresh ideas and your dd does too!