I live in Wokingham, and yes Langborough Road is notorious for bad traffic. No idea if the new Southern Distribution Road will make any difference. I am not aware of ambulances using that route as there are always cars parked on the road as well as the bollards up towards Murdoch Road being an absolute pain to get through.
Are you set on Langborough Road? It is very central, yes but where we are it is a 15 minute walk into the centre of town without the traffic issue.
In answer to some of your other questions, traffic in Wokingham really does depend on the time of day, where you're going etc., so for example, we live in North Wokingham, near Cantley Park - we wouldn't dream of attempting to cross the Railway Line at Easthampstead/Finchampstead Roads during rush hour/peak times because of the traffic; also Reading Road if they're digging it up can be a bit of a nightmare.
Childcare - our son goes to Muddy Ducks Nursery, which is based at Dinton Pastures; the childcare offering in Wokingham really does depend what you're looking for: full time/4 days/term time only etc., the Council website has a list of registered childminders - it's worth going to the individual childminders directly as they don't update the website with availability regularly. There aren't many nurseries in the centre of town due to space, so you might need to be willing to travel.
I think Wokingham is a great place to bring up families - the council have been redeveloping a lot of the play parks - Elms Field, Cantley, and the country parks (Dinton and California) are all great spaces for kids to run around and blow off steam. The leisure centre is also relatively new - there's a splash pad next to the training pool, and they run active bounce sessions (equivalent of soft play) regularly. There's also Pirate's Landing for soft play, which is really good -nice and airy, and they do deep cleans every week.
Happy to answer more questions - either on here or DM.