Hi Lucy,
First off, thank you for 'loaning' your husband to the service of our country. I am a vet and know firsthand that the families of servicemembers make sacrifices beyond what most of us would imagine. Your support for your husband, and your efforts to do the best for your family are very valued and appreciated.
I've worked with kids for a long time and while I am a mother of only one, I have nannied for growing families. Here's what helped me:
1. Wearing the baby. I personally liked using front packs when babies were little (after the first 2 months or so) and then backpacks when they got bigger. Keeping baby attached means that baby's more likely to be satisfied and feel connected while you play/interact with big sister, and allows more freedom for your hands. This works great both at home and if you are out at an indoor playpark/mall, etc. No worries about grabbing baby+stroller and trying to keep up with your older tot.
2. Open-ended 'storybooks'/quiet books. I have made these for my toddler rooms and several families. Find an old photo album (one with the sticky pages) at a junk shop and go through some magazines (Nat'l Geographics are great for this) and cut out interesting pictures. Wildlife, people, situations (fire, waves on a beach) anything you can talk about. Then put pics in a book and have them handy for when you are nursing. It might seem a little simple, but it will give you and your daughter a lot to talk about--even if you do most of the talking.
3. In other cultures, people have kept their babies snug to them out in the cold, and they've done fine. If you are wearing baby under your jackets and have a hat on baby, baby will do okay being outside for a while. They do need warmth, as they can't regulate their own body heat for a while, but unless you are exposing them to frostbite weather, chances are an hour park trip will be okay.
4. Look for indoor opportunities to walk/play. Many towns have a parks and rec department and an indoor play area for kids at a low per-visit cost. Sometimes churches host indoor play areas and you buy a membership to use the space. Do some searching around for this. The mall is also another place to walk, walk, walk around. Bring your stroller, too, for your older child if need be (tantrums, etc.) because containment will be very important, esp. if you need to change baby's diaper.
5. Have easy entertainment on hand when you go out. Besides the stroller, your older toddler will need a small bag of a few favorite board books, a magna doodle (no losing crayons/running out of paper) and something other interesting playthings. Odd ideas-- a rubik's cube, a sheet of garage sale stickers, those 'wands' with liquid and glitter in them....
6. IKEA has some great, inexpensive 'blow off steam' things like collapsible tubes/tunnels and tents. You can make an easy 'obstacle course' with a few of these things and some painters tape on the floor. Use lines of tape to "jump over the lines", x's of tape spaced farther apart to encourage 'big steps', ect. (My toddler group would happily do "jump in the square, jump in the triangle" etc. with shapes on the floor. Not nearly expensive as a game of Caboodle!)
7. Try to create a routine for dishes, laundry, etc. and have your daughter help as much as possible. Usually, when we begin our housework, we push our children off to other activities. They are very able to help us load up washers and driers--we hand things to them, or they hand them to us and then they are put in. Can your daughter stand on a low stool and play in the water while you do dishes? I often reverse the sinks when I do this with kids, so I'm next to the dishrack with the soapy water and they play in the 'rinse sink' away from the dishrack. This ensures that clean dishes don't get pulled back out. Kids are happy to wipe a floor with a wet sponge.
8. Get out the playdough. I can't stress this enough. Playdough, at a low table, is a lifesaver. Don't spend a penny on 'playdough toys' however. Instead, use old chopsticks from take-out, popsicle sticks (you may want to buy craft sticks), and whatever is in your kitchen--potato masher, meat tenderizer, spatulas, etc.-- and offer these sorts of items. At this age, kids aren't interested/capable of doing the "roll it out, cut it out' as much as they are just exploring the dough and sticking things into it. You might need to warm it up a little in your own hands to get it started, but once they start putting sticks in or figuring out "I press this tool in and it makes a pattern on the dough"... then, they're off.
9. The Snack Box. I love the snack box. Toddlers are odd eaters, and it helps to have a little container with a half-sandwich, prepared fruit, nuts, cheese, a bit of cracker or pretzel and carrot or other favored veggie to pull out when they say "I'm hungry". I would use a sandwich-sized container for this, and stock with healthy food. (No cookies, candy, chips, etc.) This way, if you find yourself behind the 8 ball and need to hand their snack box to them in lieu of a meal (fussy baby, etc.), you won't be worried about ruining their eating habits or if they've missed the more healthy meal.
10. Lastly, I'm going to suggest calling on your good friends to help you out. The friends who are okay with the house not being tidy, the ones who don't expect a lot of fuss being made over them. Friends you could go camping with, because they don't mind that you didn't get your hair and makeup or a shower together. Ask them if they are available to help-- and thank them profusely when they do. (A card or appreciative email is nice.) Sometimes this will be coming over for an hour so you can take a quick shower and start dinner. Sometimes they can take your daughter for a walk or a special trip out. Or maybe they can take baby when baby's a bit older, so you and your daughter can have some time together. I hope you do have someone in your world to help with this.
Blessings to you-- I hope there was an idea or two here that you can use!