Your new wife knew you had children from a previous relationship. When she chose to marry you she married your children as well.
If she can't accept that then she isn't being responsible.
Always, put your children first. They came first!!
Your children are a gift to you and they are also your heart, your life and your responsibility.
If your new wife can't accept your children and she choses to leave then she wasnt the woman for you... If she loves you with her heart she will do what it takes to make things work.
Family counceling is a wise consideration.
I personally come from a blended family. My brother and I would live with our dad and his wife and her kids during the summer months.
It wasn't easy. I look back and I many times wish we would have had some kind of counceling to help in the transition.
My step-mother didn't want my brother and I either. She didn't even like it when we visited on the weekends. She put on a fake face when dad was around and then when he was gone she treated us like crap.
Now that I'm older I see her in a different light (possitively), even though I still don't trust her entirely.
I,-- also being a single parent and have dated men in LTR who also have children --, know first hand from both sides of the situation.
I am a child of a broken and blended family.
I am divorced with a child who had dated men with children.
I also dated men who couldn't accept my son and treat him with kndness.
Its a difficult situation. The best answer is to work at it. See counceling for EVERYONE... Individually as well as in a group(family). Set up structure, rules, boundries, space, reasonable expectations and most importantly remember everyone is unique, individual, has their own personality, interests and manners.
Counceling will help in this.
I went to relationship/family counceling with Xbf who had 3 kids and I had my 1. We were together for 4 1/2 years and the kids bonded with me more then he and I did.
(I miss his kids terribly--I feel a vacancy without them in my life and its been about 5 years they have been out of my life.)
I do understand the dynamics and I also can see how it can work out and how it can fail...
If your current wife can't make an effort to make this work then she isn't the woman for you... Period.