I'm jealous that my kids call their step mother mom
Do you feel like they think she's a better parent than you?
She lets them eat sweets and I don't.
It's understandable for you to worry about what your children think of you. Just because they like their stepmother doesn't mean you are not the one they consider to be their mom.
So I should let them eat sweets to win their hearts?
I believe it's best to just keep parenting the way you are, you don't have to give in to what they want. Their opinions of you may matter a lot, but in the end they will appreciate you looking out for their well-being.