It's ok - you are going to be fine. :) Better than fine actually - you are about to give your oldest child the single greatest gift any parent can give a child (in my opinion) - a sibling. Everything will be fine. My oldest was 2 when I had baby #2. Yes we had 2 in diapers for awhile - so you change 1, change the other, then go on. Pit stop style. :)
Credit card - take the $1000 or $1500 or whatever the amount is out of your checking account or savings and pay that down now so you aren't also paying interest. Register at mint.com for your monthly budget. You plug in your fixed expenses - in this case being the cost of of the monthly daycare bill for both of them (you have at least a few months though before #2 starts so you can actually do this during your maternity leave). Also plug in rent or mortgage payment, break out bills (cell phone, utilities, car insurance monthly, as well as property insurance and property taxes if applicable broken down by 12 so it can be factored into your budget monthly and it's not a big ugly surprise when the bill is due). That way you know exactly how much money you have extra each month and it's not stressful. I can see exactly how much is left in my budget - I check it every day...and if I'm getting close to the budget number, I'll skip that latte or trip to Toys R Us and get it next month. Also consider switching to a bank that gives you 2 debit cards, or get in the habit of paying down your credit card balance every month (esp. if you can earn miles by using the credit card).
And as for things to do during the summer, parks and playgrounds are free! :) Your newborn is going to be super easy to travel around with. You guys can spend the day at the park without spending a dime - that's just one of the blessings of a summer baby. I always loved just bringing a little cooler of snacks & drinks, a big blanket, some toys, and bringing my kids to a park. My son would just run around and play, stop and have a snack and read some books, and basically tire himself out. I would nurse the baby discreetly then she'd fall asleep - I always brought her snap & go stroller so I had her carseat with us - nurse her, change her diaper, put her in the carseat with the sunshade up, and we had 2 hours to chill. :)
Congrats! You're going to do great.