I have a 2 1/2 year old as well, but she is my third vs. my first so there are things I have learned.
The first is that you do NOT need to spend every waking moment fully engaged with your child. As a matter of fact, you may be doing him a disservice by starting that trend. Kids really need alone play time . . . it allows them to stretch their imaginations, is an important part of the self-soothing process, etc. And don't get me wrong, I was very bad about that with my first child! But my little one has a great time just looking at books on her own and pretending to read, playing with her toys, etc. She also has become quite savvy on a computer and we have some great educational programs. She insists on using the computer on her own! And this is not to say we don't have our together play time because we most definitely do.
As for schedule, I think the better term is "structure." Generally she wakes around 8:30 a.m. and eats around 9:00 a.m. Usually after that she gets dressed. Then it's hang out time . . . books, toys, etc. If it's nice out, we may go to a local park or just play in the yard. There's a weekly book reading at the library which we try to go to. Lunch is around 12:45ish. Put her down for a nap around 1:30 p.m., and if she decides to sleep then I get her up around 4:00 p.m. If she doesn't sleep I let her rest for about an hour. Dinner is around 5:30ish. Usually she gets some computer time either before or after dinner (before can be helpful because she's entertained while we're making dinner). Bath time is about 7:30ish. Bed time is by 10:00 p.m.
We throw in the occasional visit to Chuck E. Cheese or Wiggly Play Place. And of course there are those days where errands need to be handled and she must come along for the ride! Cleaning is done on Saturdays . . . my husband usually takes my little one out of the house for a few hours. Laundry is done during the week, on no specific schedule. House is constantly cluttered but not unclean. I HATE the clutter but honestly no one else seems to care so I've learned to live with it (to an extent) because that's just what you have to do . . . don't become OCD! And taking care of a child full time is harder than any job outside the home, so cut yourself some slack! You are doing a lot!