The foam roller is what gave you the rougher finish. Sanding was needed after the first coat. If the first coat is not flat the following coats will not be flat. The high quality brush should have been used for the first coat.
A sprayer usually yields the smoothest finish but a brushed or wiped finish can be just as smooth if sanded between coats and rubbed out afterward. Rolled finishes are usually best on textured walls and exteriors where a super smooth finish isnít so important.
If you don't have time to do it right the first time, when will you have time to do it over?