It may not be a good idea to force her to eat ..this will create the vomiting for sure .as she doesnt do this with others I suggest that you do take her to the Doctors so he may see what is going on, it could be a stomach bug going around .,that has reinfected her. Be tolerant and when you put her food down let her be in control of eating, do not make her eat food she doesnt like .
A 4 year old will not make herself vomit. Something is going on and you need to get her checked out. If YOU are the only one forcing her to eat, there may be some type of anxiety occurring as a result and this is why she vomits only around you. Four year olds are picky eaters, and as frustrating and worrisome as it is, you cannot FORCE your child to eat. It's not right to make her clean up after herself and take away her TV privledges for something she has no control over, and you are compounding the problem by doing this! A tummy bug is her only reasoning as she is only 4! She has no idea why this is happening, but it definitely is not on purpose. Please take her to her pediatrician regarding this, something is wrong.