How old is she? Most of my kits are 400 grams by 4 months... I am not an older breeder as I have only been breeding and showing for 4 years but personally, I don't breed any females under 600 grams and of all my breeding females, my average is around 800 grams (My lightest is ~650, most are 700-800, and a couple are 1000-1100 g). Breeding a female who is too small can potentially lead to some serious problems. If her pelvic opening is not large enough, she will be unable to safely deliver kits. I don't know how old she is but if she is over a year and only 420 grams, she most likely will not grow much anymore and not a chinchilla I would consider breeding. It would be a huge risk to her life.
Reading about your vet's advice for Schroeder, I would definitely look for a new vet. Cat laxatives are not good for chinchillas. A chinchilla who is in ileus (a slowdown of the digestive tract) and in danger of going into G.I. stasis should not get those oily cat laxatives. Not only do those lipid-rich cat laxatives slow down gastric emptying, it also contains a lot of sugar (corn syrup and malt syrups) which can cause bloat, a bloom of Clostridium bacteria, and further G.I. upset. Once a chin develops bloat along with G.I. stasis, it is a very difficult road back to recovery. If they don't get frequent handfeedings, motility drugs, subcutaneous fluids (and water offered via a dropper), abdominal massages, and simethicone (infant gas drops), they often do not recover... it is an around-the-clock treatment, often for up to a couple months until they are completely better.