Mine are 16 months apart. The oldest now 20 months.
If you try to leave the house before 11am with your DD2 in the buggy will she then fall asleep instead of needing to be fed? Would this give you some time with DD1?
We all get up in the morning at stupid o clock with the toddler, and are all washed, breakfasted and dressed and ready to leave the house by 8.30, when DH leaves. Would this work for you? It's the actually getting us all out the house that's hard, so I don't try to do it on my own.
I can then manage the two on their own for the morning as we will head somewhere easy like a park or supermarket. If the baby wakes up then yes, I sometimes fed her in the sling (she was big too) although at 4 months now this doesn't work any more.
We come home, the toddler naps and the baby spends this two hours feeding constantly (less so now, but certainly when she was younger).
The toddler wakes, has lunch, and watches TV while I try to get up all ready to go out again.
In the afternoons we often do things like visit my in-laws (I know, I am very lucky here!), mooch around a shopping centre or go to the park again.
Dinner is a mess still, the toddler gets cornflakes in front of the TV, but well, we'll sort that one out in it's own time. Also stays in front of the TV while I bath the baby, then the baby sits in a vibrating bouncy chair while I bath the toddler and put him to bed. Try to find something like this that will allow you to put the baby down for a few minutes.
Sometimes yes, while the toddler is trying to go to sleep I feed the baby. The toddler has just about got used to this now. It also helped that the toddler was transitioning to one nap when the baby was young so was knackered by bedtime and went to sleep really quickly.
Well, that's how I cope. Hope some of these ideas are useful.