You do not split a family apart. You do not invite one spouse and not the other, and in the case of family, you do not invite only the children you are related to by blood and ignore the step-children , and use a limited budget as an excuse to do so.
Where did that young lady find her manners...in a Cracker Jack Box?
What you should do is decline for yourself and ALL your children, and tel your husband it's up to him if he attends, but your children will not......you will not tolerate anyone splitting your family apart....
...or just you & he go and ALL the children stay home.
Besides being a terrible thing to do, think of how the uninvited kids will feel...like only the youngest 'counts' and they don't.....which as far as your SIL is concerned, is true.
Some things are just plain wrong and this IS one of them...."My wedding so I'll invite who I want and not invite who I don't want" is no excuse for playing favorites with kids or rejecting some children within a family unit because they aren't blood.....and I guarentee if she had kids and this was pulled on her she would be howling like a banshee.
I have four kids, and yes, they all have the same father-but if they didn't and this was pulled on me, I wouldn't tolerate it. My response would be "Well, since your budget is so tight you feel you need to play favorites with my children, I'll make it easy for you....NONE of my kids will attend as I will not have any of them singled out for rejection, even if it's just a wedding."
You don't have to be that outspoken or even rude...just accept for yourself & your guy.....decline for ALL your kids....if she asks why not the youngest, merely say " My children will NOT be treated unequally, or will favorites be played with some....either all attend or none attend." You are mother, you have this right.
If she isn't aware of how hurtfull this is to all the kids involved, then she's an idiot...the youngest will feel guilty over being singled out & priveliged to go & the others will feel they are not good enough which is why they were rejected.
Pity any kids she may have, the gal is clueless.
And she does need to be called on this. There are ways to cut a wedding guest list. Ostrizing kids because they are step-kids and not blood while invited their sibling who is blood is NOT the way to do it.
I guarentee any child psychologist will tell you this...wow, what a prize she is.....shame on her.