I have 3 boys who are 26 months apart, the youngest are twins so I know what you mean about not being able to hold onto everyone! Is your backyard fenced in? We used to play in our backyard quite a bit. Sandbox, Little Tykes castle-playhouse, the usual plastic trikes, wading pool, etc. My neighbors commented once that they thought I was doing daycare at my home but it was just my kids! Sure kept them occupied and you don't have to worry so much since it's within a secure area. Later, when they were older, they had friends over and the mom's and I would sit and chat while the kids played.
The other thing my boys loved was the science center here in Orlando. There was a kiddie area with water play, age-appropriate activities, etc. and a guard at the entrance who didn't allow anyone to leave without the parent and a wristband check. Is there something like that in Jacksonville? The annual membership is affordable, even if your budget is tight. Discovery Zone was another good one. We would go once a week and play. Many times they have discount mornings...
Does your church have "mom's morning out"? You could leave your littlest and spend the morning with your older child. Fees are usually minimal. It was a lifesaver for me! If you don't necessarily have a church of your own, many local churches accept non-members children.
My last suggestion is a playgroup. Check your local newspaper for information in the ads about playgroups, check with friends, bulletin boards at your pediatricians office, the YMCA, etc. Playgroup mom's help each other out at the park and sometimes they have playgroup at someone's home. Good for mom to socialize a bit, good for the kids to have friends. Good luck!