I moved to Austin about 6 years ago now and have really enjoyed my time here. Like most cities, the different areas of town have very different feelings to them. I really like where we live now - southwest Austin (the area known as Oak Hill). It's very convenient to downtown, there is a nice mix of housing (from apartments, older homes, McMansions, etc) - and the traffic is a lot better. Austin has a bad rep for traffic, but compared to other cities I've lived in, it isn't really an issue, but I do like to avoid I-35 (the main north-to-south corridor) at all costs. The northern suburbs have great housing prices and good schools, so they are very popular with families. Although the east side (anything east of I-35) has been going through a transformation, I wouldn't recommend it for families yet - the schools aren't that great and there is a lot of crime.
It gets ridiculously hot here - this summer has been a cool one (95 to 97 degrees all this week) compared to last summer where we had like 60 days straight of 100+ temperatures. That is the thing I hate the most about living here, because it is a very fun outdoors town, but being outside in the summer just sucks. But it stays very nice the rest of the year and it doesn't rain a lot - so if you've ever wanted a backyard pool or a convertible, you're in luck.
There is a lot of family-friendly stuff here in Austin and fairly close by. It is a very educated city so there is a lot of culture for a city this size (ballet, opera, museums, plus the famous music scene). Most people in Austin aren't from Austin, so I don't think you'll be alone in not having a lot of family around. The cost of living here is higher than a lot of places in the south, but still very reasonable (nothing like the northeast or California). It all depends on how you want to spend your money - you could spend $500K for a fixed-up 2 bedroom downtown, get a McMansion with five feet of space between your house and your neighbors, or buy a ranch with 15+ acres. But the median is much closer to $200K for a regular family house. Prices for stuff is very similar to Florida, but home prices are definitely lower.
Schools run from mid-August to late-May, early-June. The major breaks are Thanksgiving (late November), Christmas through New Years, and Spring Break, with a couple of other small holidays thrown in.
Frankly, health care compared to Scotland is probably going to be kind of a shocker. Is there a way your parents could just come stay with you like 6 months out of the year, so they could keep what they have now? Most retired people here get help from the government in the form of Medicare to keep their costs low, but a friend of my parents recently retired and is still 3 years from getting Medicare and their insurance recently was raised from $600to $1200 a month.
Sorry about the long post - feel free to PM me if you have any other specific kind of questions.