Not sure I can help you too much,because I cannot see your actual hookup, but I can tell you that the important things are
1. That the hose reach from your machine to the drain pipe with no stretching or stress
2. That any connections you have, try to set them up so that connecting piece goes inside the next piece in the direction the water is flowing
3. That you discharge hose empty higher than the drain from the machine so the water does not siphon out when the machine fills.
The smaller diameter should not be a problem as long as the above criteria is met.