D.P.
Hi there. I went through the same thing with my now 6 year old daughter, but her's was ketchup. I went as far as asking others what to do...but was asked, what's the big deal? As long as she is eating. And it's true. Nothing wrong with a little applesauce or yogurt. Sounds like it's become a power struggle and no offense, but to have a power struggle with a 3 year old is pointless. Your Mommy and you fix the foods...I'd say let him have his applesauce and eat it too! lol
(and yes, Terra put ketchup on EVERYTHING...including ice cream, bananas, toast etc.... I was afraid she'd be spoiled if I gave in, but my kids are one of the only 6, 7 and 8 yr olds I know that consistently say yes maam, no maam, and please/thank you) God Bless you.