From vienna to infant jesus of prague church

long way for a day trip,if coming by car you are looking at 4 hours each way and then you won't be able to park anywhere near the church,so may have to use one of the park and rides on the outskirts of the city and the metro from there.
quite frankly I do not think this is a viable day trip from Vienna

Car would be quickest but you could also do it by bus or train (5-6hrs each way). You wouldn't have much time in Prague, maybe only 3 hrs or so, and it's a long trip for such a short time. But, if it's important to you, it's possible. Check rome2rio website to see the bus and train options, then check the bus or train company's website for costs (don't rely on rome2rio cost estimates). You may decide that it's too time consuming or too expensive to make it worth it.

Trains run direct between those cities and takes 4.25 hours each way, starting from 7:00 a.m. Longer timing provided by Rome2rio is another fail for their search results; they can't do everything. How to Look Up Train Schedules and Routes Online gives you the recommended DB train schedule link and tips for using it.