Trying to Figure Out How to Balance Part Time Work and Time with My Toddler

11am is a bit early for a 2 year old to be napping, but they are all different, and yours wakes up early too. Why don't you put him to bed later, since it's going to be summertime and you'll have more time to spend with him all afternoon and evening. Then he'll sleep a bit later and take a later nap, which will give you some time to yourself in the afternoons for cleaning, resting or whatever. 7:30pm is pretty early when it stays light out until almost 9pm... We went through this all too. But we found when our son was 2 that it was much nicer to have all evening together and not have to rush dinnertime & bedtime every day. We could be out on walks later in the evening, which was great for all of us... And the later bedtime helped out son sleep better anyway (he was still waking up at night with earlier bedtimes...)
If you can work mornings each day, then come home & have lunch and playtime with your son for a while (trip to the park... walk... whatever) then try naptime closer to 1pm. It worked really well for us most days...

Firstly, I think any way you can best manage the inherent juggle of life and work with kids that makes sense to you is the way to go!
With napping...and most of my son's same-aged friends have followed this pattern....once it was one nap, down by 12ish, nap 2-3 hours. Time for fun in afternoon, bedtime more around 7pm. BUT as my son and his buddies approached 2.5, nap time was pushed to be more around 1pm (sometimes even later), and I kid you not, some days its *well* over 3 hours and he's still snoozing away. Bedtime is usually a tad later - 7:30-8pmish. Wakeup times are no different, its still way early (6-6:30am-ish!). It has been a bit harder to have him napping later in afternoon. If he's not up until after 4pm, it doesn't allow much time for activity before dinner. This was especially problematic in the winter when it was dark by 4:30 too! In general, he's a happier camper in the morning, so that's when we get the most accomplished (errands, toddler classes, playgroups, general fun). And its predictable. You never know exactly when the nap is going to begin/end, even in the most structured of settings, so I have found it much more difficult to plan anything for the afternoons and like to keep that very loose.
In terms of how an older toddler's patterns may affect your work scheduling, it may sort of be a "six-of-one-half-dozen-the-other" situation. Do you want to juggle your child care/work every day or just 3 days a week? A good friend of mine went from working PT every day to 2 full days recently and really likes this set-up. Her kids get a full day at the caregivers (breeds consistency for their days) while she focuses all of her attention for 2 full days at the office. When she's not working, she feels like she's very focused on just her kids, instead of abruptly changing roles throughout the day. That said, if you worked mornings, had his nap time "off" so you can use it to catch up on other household/personal matters, you could probably still make afternoons work with your son since you will be focused on just him...in general, I do believe you can make whatever work. Even a car ride or a trip to the grocery store can be quality time if you make it so!

I would like to echo what Jennifer is saying, that really the most stressful part of working is getting going in the morning, commuting- just generally getting out the door.

Currently I am a full time teacher, wishing I could be part time. My ideal scenario would be to work 3 days a week. When you are at work you can really focus on work and when you are with your son, you can really focus on him. I would think that doing half days would be exhuasting, you'd be running around everyday for 1/2 pay. Just my opinion!

Yes, as toddlers get older their naps become later and later. My son, now 27 months, naps at around 1-1:30 until 4ish.

I also have a strong opinion in regards to working every day for 1/2 a day verses 2 1/2 full days. I did the ever day thing and found it very difficult. Granted it was a new job and I wasn't that into it, I eventually left that teaching position. I just felt that all the morning prep and stress of getting out the door and getting to daycare, and then getting to work was so difficult when I would only be there for 3-4 hours and then have to get home or to an activity with my son. I also realized, like you are, that at some point he would need to nap in the PM and I would really miss the majority of his day. I will soon be interviewing for a 2 full day a week position and know that this set up would be so less stressful. I would only have to do the morning routine two times a week and not five and then I will have 3 full days with my guy, that is if I get the job. Anyway my advice would be to stick to your current schedule. Just think about what you do 3 times a week and now picture it 5 times a week. Good luck with your decision.