I can relate to some of what you say and two things come to mind. One is that you might be trying too hard and the other is that you might benefit from a social network of other mums and kids. I belong to a casual neighbourhood network of mums. Every now and again one of us sends out an email - playdate at my house/this park from 10-12, and whoever can come, shows up. We talk about anything and everything while the kids play (or fight!). I love these mornings cos I don't have to think about how to wear my kids out for nap time (they are one and two), plus I get some social time. They are so excited to go to someone else's house and play with new toys and see other kids. (BTW this group was started by a lonely mum who put an ad in the neighbourhood newsletter calling all other mums..._)
As for trying hard to provide the optimum entertainment for your little one, remember that their expectations are quite different from ours. She may have just as much fun pulling all the clothes out of her drawers whilst you are trying to put them away, and while you might not get any tidying done, you could teach her colors for example.
Anyway its soon about to change. My 2 yr old loves washing up.
I fill the sink with water and various kitchen items and she is totally content to wash the dishes for a while. Sometimes I even give her dirty ones and they do get a bit cleaner. And so does the floor cos I have to mop it afterwards. I promise you, she will soon start playing more independantly!
Involve your child in what you have to do. She will enjoy it if you involve her and you won't have to arrange your day completely around her.
One last thing, are you possibly a little depressed?
I think it takes a bigger toll on our bodies to have kids in our 30's. Late 20's are said to be the best time to have kids, mature enough and bounce back quicker. I had mine at 34 and 35 and I suddenly aged alot and it changed my identity!
Also have you left behind something you are missing?
A career, some independance?
I was halfway through a Masters in Chinese Medicine when I became unexpectedly pregnant with my first and then almost immediately pregant with my second. I adore my kids and would not want anyone else to take care of them at this young age, but I recently resumed my program at 6 hrs a week and this is my sanity!!
Maybe you could find something that you do once a week that helps you connect to yourself, as an individual.;
I notice that I refer to myself as "we" cos I almost never go anywhere alone. That says something! Sometimes you just need a break to be you. And if it's a weekly thing, you can loook forward to it.
All the best