Hi I.,
I can't remember when I started getting engorged in the mornings, which meant I had an excess supply of milk that I could pump off. You may not experience that for another few weeks.
Please see a lactation consultant. They are a wonderful help to any breastfeeding mom.
My consultant had me pump after every feeding to start building up a supply. At first I only pumped a half ounce or so, but it gradually built up to where I was able to stop pumping after every feeding and I only pumped once in the morning for 5 minutes, and I got 3-4 ounces that I froze. When I went back to work when my daughter was 3 months old, I had a freezer full of milk. I pumped every three hours while working, and I pretty much kept pace with her until she was 9 months old or so. At that point, I was glad I had the freezer stash because we started using it up. My daughter is 15 months old and drinks whole milk during the day at the sitters, but I've cut down to only pumping twice a day to donate breastmilk to other moms and to have an emergency stash for when she's sick.
Please see a lactation consultant. If you can't or don't, try drinking Mother's Milk Tea to increase your supply, take Fenugreek for the same reason, and pump after your feedings.
Yes, of course you can nurse her when she's with you and give formula when she's not. Just realize that nursing is a supply and demand relationship, so the less you nurse the lower your supply will get. If you start to skip the morning and evening feedings, your supply may dry up. If you want to go out to dinner and you'll miss the vening feeding, pump when you get home to maintain your supply. One of my friends went back to work and didn't pump during the day. She breastfeeds at night and in the morning, and her daughter is 14 months old. You can do whatever works best for you.
Good luck!