I've been bike commuting w/daycare trips for almost 2.5 years now. What I found works best is, yes, to drop kid(s) off at daycare, then bike in to work. For me daycare is 2.5 miles away, then work had been ~12.5 miles, and is now ~9.5 miles from daycare (changed jobs).
You can definitely do this! You will have great memories and this is such a fantastic way to carve out some time with your kids during a busy working parent's life. We have many discussions about various trucks, bridges, changing seasons, trees, animals, and MANY MANY sightings of GARBAGE TRUCKS!
My progression was something like this:
1. baby <10 months: walk to daycare with baby in body carrier & pushing bike alongside, then bike in to work; took a long time but was very pleasant.
2a. baby 10-30 months, nice weather: bike to daycare with child in bike seat. I got one of these:
http://www.weeride.com/Kangaroo-Center-Mounted-Child-Bicycle-Carrier, and like it a lot, mostly because having the kid in front of you makes it easy to have a conversation. It is rated to 35 lbs. Leave the bike seat at daycare during the day (it is fairly small, so I just brought it inside and put it with the rest of their clothes/gear), bike the rest of the way in to work as normal (though the bar for this kind of seat stays on and is a fair amount of extra weight). If someone else does pick-up they can easily take the bike seat too.
2b. baby 10-30 months, bad weather: When temps got below 20F my child started to complain. That winter was really icy too so I ended up a fair amount of the time just driving home-daycare-back home then doing a bike commute, then doing daycare pick-up by car. Sort of annoying...
3a. kid 30+ months, nice weather: same deal with bike seat
3b. kid 30+ months, bad weather: I then got an old Burley trailer and he was fine in that this whole past winter (it was -15 F some mornings). I detached the trailer and locked it at daycare during the day. Harder for someone else to take the trailer home if you aren't also doing pick-up. I (correctly) anticipated slipping on the ice; the couple times that I went down it was fine because the trailer just stays upright.
4. Soon the kid will be too big for the Weeride bike seat. I recently got a Trail-a-bike off CL and I plan to lock it up at daycare like the trailer during the day.
5. We have another on the way too. Not sure about this yet... might do more walking with both of them, or carry both in the trailer, or do a bike+trail-a-bike+trailer train.
There is lots of debate and many opinions, but very little evidence, about a "safe" age to start biking with a young child. Maybe there will be a few months where using the car is the best option before you feel comfortable biking with your newer little one, but I would think a bike trailer would be fine after that period. Somehow to me it feels safer to have another older kid back there too.