Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I am very sorry to hear about your pup's eating green plants and vomiting.
Dogs with nausea or gastroesophageal acid reflux often eat plants or foreign material to make themselves vomit. They will often swallow repeatedly and lick things trying to soothe their nausea and acid burn. If they can rid themselves of whatever is irritating their stomach that way then all is good.
But when they are vomiting repeatedly and continue to be uncomfortable then we need to stop them from eating any more plants. It becomes a vicious cycle where the more they vomit the more their stomach acid burns their esophagus and the worse they feel.
Possible causes of vomiting and nausea causing them to eat plants include a change in diet, dietary sensitivities or allergies, or eating things that they should not like too many fatty table scraps or garbage, bones etc. Addison's which is a poorly functioning adrenal gland is another possibility for waxing and waning vomiting and nausea. If she's a younger pup metabolic organ failures (kidney or liver disease), pancreatitis, inflammatory bowel disease or even infiltrative cancers are possible causes but less likely.
Has she eaten anything she should not have recently (toy pieces, bones, garbage)?
Any changes in food or treats?
You can give her acid reducers to try and settle her stomach. Either:
1) Pepcid-ac (famotidine) at a dose of one half of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one half of a 20mg tablet per 20 to 40 pounds of body weight every 24 hours.
These will reduce stomach acid and should help settle her stomach. These can be used as needed if necessary as they are very safe.
I'd also pick up her food and water for now. A couple hours after the acid reducer is given you can offer small amounts of water or ice cubes to lick. She's likely thirsty but we need to settle her stomach first.
No food for 24 hours. Small amounts of water only.
After her 24 hour food fast then start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken) and 2/3 boiled white rice. Give small meals several times a day. Feed the bland diet for several days and if she is doing well, then start mixing in her regular diet and slowly convert her back.
If her vomiting or nausea continues then she may need injectable medication from her veterinarian to get her stomach upset under control.
So watch her for continued vomiting even with the acid reducers, blood in her stool or vomit or a fever (more than 103.5F rectally), a tense painful belly or lack of appetite after her food fast. If any of those occur it is time to seek hands on veterinary care.
If this has been a repeated problem for her consider whether she has been getting different treats or lots of table food, or have you been feeding a different diet?
If you go back to the original food, stop table food and treats and her nausea continues even with the acid reducers, fast and bland diet then you may wish to consider using a sensitive stomach diet such as those made by Science diet or Royal Canin.
If that doesn't seem to be effective perhaps using a low irritant prescription food, like Hills i/d or Purina Veterinary Diets EN, or a hypoallergenic food such as Hills z/d or Purina Veterinary Diets HA long term will help. She may have a dietary allergy or a sensitive stomach. It would also be a good idea to have blood tests done as well to make sure there isn't an underlying metabolic problem like pancreatitis or Addison's disease present if this persists.
Please let me know if you have any further questions.