Sounds like you need more than 2 coats of paint. Red, as well as yellow, are very transparent colors and will require multiple coats for perfect coverage.
Some things that will effect a colors ability to cover.
1) Deep tone and bright colors must be mixed in "deep tone" bases. This paint base has very little titanium oxide which adds hiding to the paint. Try to choose a color that can be mixed in a medium or pastel base.
2) The sheen affects a colors coverage. Flat sheen cover better than satin and semi-gloss or gloss are the worst.
3) The tools you use also affects coverage. A good 100% lambs skin roller is better than a cheap synthetic. Also, the best coverage is achieved when spraying instead of rolling.
4) The better the paint the better it will work for you. Always choose the best paint that you can afford.
The bottom line, you need to apply at least one more coat.