So, based on your monthly expenses, you're looking at $1600/mo in savings or to put towards annual expenses. Annual expenses, for us, are things like vacations, Christmas, and life/disability/auto insurance (b/c we're billed annually or semi-annually for these).
For the vacations / visits, I would calculate a reasonable amount to spend on those trips, divide it by 12, and have that amount automatically deposited into a savings account each month. I find it's easier to sit down w/ MH and figure out how many times a year we'll travel to see family if it's a big (overnight) trip.
For the "working to pay for childcare" issue, I absolutely understand where you're coming from. It seems like a losing proposition. But if you would like to work, it has a long-term payout to start sooner rather than later. If you can afford it, even work at a loss for a year or two. Daycare expenses will go down. But in the meantime, you will be gaining valuable experience, making important connections, and maybe even getting a raise or two in the meantime. Sheryl Sandberg's "Lean In" discusses this. You will find that opinions in this forum on this issue run the gamut, so it's important to come at the issue understanding how YOU feel about it -- not other people.
I'm not clear on whether you're giving up the car or not and whether the rent amount you quoted is an actual amount in a location where you've decided to live. Which car would you give up -- the one with the loan, I hope? I'm not a city dweller, and even less so since having a child, so I wouldn't move to the city simply to avoid paying for gas. We drive a Prius and it's treated us really well so far in terms of gas expenses and maintenance (knock on wood!)
About the new clothes ... when are you moving? If you're moving in December, then you will find a lot of winter clothes and gear start to go on sale / clearance at that point. Regardless of when you're moving, I recommend getting into town and seeing what kind of outdoor gear you'll need -- a jacket with a zip out liner or a big puffy jacket that's instantly warm, something knee-length or waist-length, etc. I've found that my coat needs change with the commuting experience (eg, waiting for the commuter train outside in the snow meant I needed something instantly warm that was knee-length. But driving to work every day I needed something waist-length that wasn't as warm b/c I didn't spend as much time out in the cold).
Kids' clothes are really easy to get inexpensively if you go to a few semi-annual consignment sales, and they happen in the fall. I'm a HUGE fan of them! Then again, if you're moving in December then you'll be able to get kids' clothes on clearance at some deep discounts.
Does it snow a lot in Delaware? If so, you'll both need snow boots. It IS hard to get a deal on those. Expect to pay $100 each for good pairs. For the coats, also set aside $100 each. Your toddler will probably need snow boots, but I wouldn't pay more than $50 for them new or more than $50 for a new jacket ... but again, if you're moving in December or you can get them at a consignment sale, you'll pay a whole lot less. (don't forget snow pants for your little one!) Also, with a toddler jacket, if you'll be driving with your little one in the car, you should get a warm blanket and use that for warmth in the car instead of putting him/her in a big bulky jacket -- they're not safe in carseats and once the car heats up, you can't take them off if your little one is buckled in.
As for the gift expenses, you could annualize that and save for it throughout the year, too. I live in the northeast, though, and I don't think we got more than a handful of $250 checks at our wedding. Our go-to cash gift is $75. For baby showers, I have been couponing to get baby supplies and wrapping them up creatively (diaper cake). Or, if you have a particular talent, you could offer that as your gift. A friend of ours made our wedding cake, and that was her gift. It was priceless, because we couldn't find someone who would bake the flavor we wanted!