I grew up in Austin, and it has been a bicycle hot spot for decades. Despite the gentrification of an otherwise awesome city in the past 20 years, Austin does have some excellent bike shops. If one LBS does not work for you, there is a plethora of really good shops there.

Unless times have changed:
-Freewheeling bicycles (on 24th near the university)
-Bicycle Sport Shop (By the Arboretum). Marty is a great guy and knows bikes. I knew him when he managed the shop in College Station and he's a solid guy with a passion for bikes. He tends to employ similar people.
- Bicycle Co-Op. If it is still there, this has been an institution.

I'd recommend finding a good shop (which section of town do you live in?) and having them help you out.
The Peloton is an excellent road racing bicycle, which may be too aggressive for your needs, especially things like commuting and towing a trailer.
If you find (with some face to face advice from someone who know something about bike fit) that the Peloton will work for you, keep it for recreational rides and as a commuting backup.

Once you've established some fit parameters, test ride numerous bikes (5-10 minutes, not just a slow circle in the parking lot) and see what suits you.
You might be surprised at how sporty some of the more comfortable, transportation-oriented bikes can be.

If you are on a budget, the Austin Craigslist should offer a steady supply of options - it's a bike city.
If you have the budget to consider a new bike, there are many options, so the test riding well help you dial in the genre that suits you.