What I do to avoid this is to do very thin, watery coats. I haven't tried this method on ponies because I haven't had to cover up marker, but it will probably work. Basically, you just water down paint and paint on thin layers allowing each to dry thoroughly. Also, if a layer is too streaky or textured, you can just buff it down. You can also buff/sand down acrylic paint you have already put on ponies if you haven't tried to remove it already. And, if you have one, you could try airbrushing? I've never seen anyone use it for ponies, but I've seen people airbrush a doll to change its body color for customizing. What I would do to airbrush is cover the hair, symbols, and blush and airbrush the affected area.