I have a few dairy goats, and am also a nursing mom. My daughter is nearly 2 and showing no signs of quitting any time soon! I also believe animals are people, with thoughts and feelings, if perhaps a bit simpler than ours, and try to treat them as kindly as possible. That they love their children, I have no doubt.
You can separate at night if you want, but I don't think you have to. I did it with one baby boy goat, starting at 6 weeks old. I put baby in a stall right next to mom, with other young goats. Mom had another adult goat for company. My stalls are built from pallets, so mom and baby could see and smell eachother through the slats. Neither seemed to mind much, even the first night. I fed the young goats at night to get them into the stall easily, and all, including baby boy, were happy to go in there and get their dinner.
I did not really get much more milk over a 24 hour period by separating them. I did get more milk in the morning, before putting them back together, but got less milk in the evening, since baby would drink more all day to compensate for not nursing at night. I did get slightly more over a 24 hour period, but not enough to make much difference. I can see that this strategy would be great though if I only wanted to milk once a day in the morning, because it definitely affects that morning milking.
And yes, milking multiple times a day will increase production, just like with humans. If you want to increase udder capacity and teat size, some people believe that separating babies at night, starting from a young age, will help with this. I have no direct experience of this (I am fairly new to goats), but here is an interesting article I read about it
http://www.glimmercroft.com/Udder.html
I just wanted to add, you might want to consider goats instead of sheep, since, from what I've read, even the best dairy sheep have lower production and shorter lactations than most dairy goats. You may not consume a lot of dairy now, but when you have your own you may become more attracted to making cheese, yogurt, kefir, etc. My little household of 3 adults and 1 child can easily go through 1/2 gallon of goat milk a day. My daughter loves fresh goat cheese, and kefir smoothies. For me, milking day in and day out can be a bit of an austerity, and if I were only getting a few cups a day it would quickly lose it's charm. For me, anyway.