I had very little time for anything until around 2007/2008 when I quit my job and started my own business with my partner. Now I can move stuff around in a way I couldn't have done before. I work more hours a week now than I ever have in a job previously, but I do have more free time. I can get up at 2 am and get work done now and free up some time the next day to hit the dry slope if I want.
Other thing that frees up time is the use of online services and technology. We use a lot of online processing services to get daily jobs done a lot faster than you could if someone was doing it manually, that must save us around 1 to 2 hours a day (banking, packaging, postage etc). Food shopping - we do that online now as well, we have it delivered to the door. Costs 3.50-5.00, but saves us time and petrol, so it's great. Although where we live now there are almost always a free DIY scanner to do your own checkout, which is better than queuing. I do a lot of clothes shopping online too now, she doesn't do as much, for her that's something she enjoys doing, so I guess for her that counts as free time, but for me, that's more of a task and with the greater choice, free delivery and free returns now on most sites, shopping for clothes online is something that can be done while eating lunch for example.
Sharing tasks is another way we free up time. If my partner wants to go away for a few days, that's perfectly fine, I can cover her duties, and likewise - she covered for me for 4 days a few weeks back because I wanted a short trip. If I feel run down, she does the petty tasks. If she's bogged down, like at the moment (she's studying her accounting qualification and has exams in 2 weeks) then I do virtually everything, even running out to buy 'feminine goods'.
We both love watching movies - so I download them in HD and watch the latest flicks while having dinner every evening, also saving time. If you want to go for drinks, that doesn't have to take all night, and you don't have to get drunk to enjoy yourself - you can pop out for a couple of drinks, catch up, and head back feeling refreshed and get still have a clear enough head to get some tasks done.
Location is another thing that saves us a ton of time. We literall have a Tesco, a petrol station, a post-office, bars etc right beside us. The benefit of being central.
If you really are prepared to make a big lifestyle change, you can have a ton of free time - this guy's book inspired a lot of people to go for it
http://www.fourhourworkweek.com/
He likes to outsource stuff, we prefer to do the opposite, we learn new business skills (web design, accounting etc) that we need so we don't have to outsource and rely on other people which slows us down in the medium term, but that's also a cost-cutting exercise and will likely change in the long term to free up even more time.
As for kids? Nanny then boarding school. Some of the best brought up, successful and respectful friends I know had nannies and were shipped of to boarding school and have fantastic relationships with their parents. If that's too expensive then re-organise your affairs and make more money.
I'd be really interested in other ways people are saving time