I'm thinking about sending my son to live with his dad.

So I just got married again and my son (from a previous relationship is taking a toll on my new relationship)
So I'm thinking on letting his dad deal with him. 
After all he is his dad right? 
And the woman that is with him should accept him for all he is (our child included) 
After all his wife is a stay home mom taking care of her own kid plus the one she had with my baby daddy. 
Why can't she just take care of mine as well? 
Y'all thinking I'm a bitch for this now right? 
Yeah but the deal is I'm the one dealing with a stepchild of a mom that thinks it's ok to just ditch her child with me because I married her baby daddy. 
*EDIT: 
I don't think y'all understood but this situation I just posted is about what my husband's baby mama is doing. Not about me.  
She's the one ditching her child with me. 
*Second EDIT:
My husband' baby mama is doing this not me. 
I posted a hypothetical situation as if it was me sending my son away.
I'm the stay at home mom with my son and the child I just had with my husband while his baby momma dichted their child with me because I'm a stay home mom of 2 of my own.