Hmmm ......
It sounds like on the comfort vs. savings balance you are leaning toward comfort. I am not sure I can talk you into anything then ....... and I can't say it better than:
http://www.mrmoneymustache.com/2011/04/18/get-rich-with-bikes/ I think you already know this, but it's possible, you can do it, and you will save a lot of $. Especially if it let's you sell a car.
We do it with 5 kids, 4 of them ages 5-10 ride on their own, and the baby rides in the trailer. We have a trailer we bought for $~80 and a tag-a-long we got for free. The kids do drag their feet and complain at times. But we are the parents, they are not. So once they learned that we simply ride our bikes, they have adjusted well! We make it fun, and a family event! We always cross busy streets at traffic lights, even if it adds a little distance, you are correct that managing young kids across a busy street is a lot.
Encouragement: It is awesome! After the initial resisting the kids have adjusted well. It's more fun (for them too), you see more and you feel better than driving! (We also sold a car and have saved a lot of money because of it)
Tip: If you are going to ride somewhere, make it absolute, don't ask the kids if they want to. Why would they want to bike over taking a car when they aren't involved in the financial aspect? (And you can be absolute about something and not a jerk about it, some people don't have that figured out). Explain to them why, they need to be part of your money saving team.
Go for it! It looks like it's out of your comfort zone, just think how great it will feel once you have a few successful rides under your belt! (Don't be discouraged if you have some rough rides at first, it will happen.)
I'd love to hear how it goes.