What does your wife have to say about this mess? Does she discipline her son? 

Kids need structure, but your home sounds like a zoo. And to heck with whichever culture your wife's son grew up in. He needs to acclimate in order to succeed in this country, and it's your wife's duty as a parent to make that happen. Take away all the electronics, turn off the d@mn wifi when you go to bed, and get that kid used to a sleep schedule so he'll have a shot at normalcy and launching as an adult.

You don't have to put up with this, you know. Recalibrate your marriage. Be the leader in your home, and require more of your wife and her son. Sit down with your wife. Tell her there's a problem and that you'll need to work together to solve it. Draw up a list of house rules for the boy, and discuss what the consequences should be for misbehavior. Tell her that you are done providing extras for such a rude, ungrateful kid and need to see improvement in his behavior. 

Stop spending more of your energy on your SS than your bio son. All that is going to do is leave you not bonded with your own child as well as your SS. 

You have made very good attempts with this skid and he is not responding. Don't damage your relationship with your child trying to appease this skid... you have been kind with both your time and money, but I think its time to disengage. 

Set boundries and rules (no eating like an animal, etc) and leave mother to enforce. 

If you’re hoping for payout for all your efforts directed towards SS you will be disappointed. Do the basics for a child who lives under your roof such as provide food, heat, shelter and transportation if his mother can’t but that’s it. You don’t even have to talk to him. I’ve gone through this with SD. Don’t expect so much from them. They are too young to know the impact of their actions. Let it go and focus on your biological child. Waste no more time, energy, emotion, or money on your wife’s child. Everytime you have an urge to spend money on SS, zap that money into biochild’s online savings account. In the future, your own bio child might act unappreciative and have a bad attitude around that age but it’s your biochild and there is a biological bond that you don’t have with SS. 

The reason I ask is because maybe your wife and son are expecting you to make and enforce the rules because in their culture it is the man of the house who does these things. 

As opposed to SMs you have a real opportunity to get your house in order by taking control.( maybe involve your wife in making some house rules with you?) It could be beneficial for your skid and dd to see some cooperation between you and your wife. Boundaries are always better than no boundaries.

Start spending more time with your wife and baby and let the teenager develop on his own more(he is at that age).

Why are you and your wife making such monumental efforts to get a neglectful father in another country to talk to his son? Maybe letting that go might be better for the kid.(would you force yourself to communicate to someone who ignored and mistreated you? I wouldnt. Why expect of SS to be ok with this). 

Skid ignoring you is how he was taught to act by his fathers actions. The more you give him attention the more he will ignore you. So just do what you would do during the day and let him hang around. That way it is his choice what he is interested in. No more xbox all day. Sports are good. Let him absorb the environment and get comfortable before expecting him to perform(some kids take more than others to adapt)

Doing for this child as you have, and getting zero response, that is so discouraging! And it sounds like you have tried everything, and more. After reading the advice here for a few years, its pretty solid. Stop trying so hard and jumping through so many hoops. Its not making things better. Creating boundaries makes you a parent, not a monster, children NEED boundaries. They THRIVE with boundaries. Take those electronics away, he can earn them back. But also note that 13 is a bad age for kids - they are not the best version of themselves I am told. I do not have any bios of my own, but came into DH's life when his were 14 and 9. One is well adjusted, the other was just really NOT. DH has set clear boundaries and I bring more structure and stability.

From what you have posted, it would seem that going over the top to get the father on board to being an actualy father isnt really working out well, I would give that one up.

Again, disengage a little bit. Spend time in the pool with your DD, and wife. SS will either join or not. If he ruined a trip, go on another one with DW and DD, and leave the bratola behind with a relative, he can sulk all he wants but he wont ruin YOUR precious family time any more. 

Time to make some changes (perhaps your screen name too?)

Imho, you need to spend much more time with your younger biochild. And, if the fdog doesn't get fed....take away video game.  And limit use of game any way..

People here are not trying to be naysayers.  They are trying to be realists.  Unfortunately, some try to use long-held myths, such as suck it up and just give it time and “common sense” when it comes to step-parenting.  The problem is, in reality little of this holds much water.  I know I'm switching gears here somewhat by focusing on SMs, but some of this holds for step-dads as well.

In reality, there are studies that show the more a SM tries to be nice to her stepchild, the more likely she is to be rejected.  “Women with stepchildren are more likely to feel compelled to try everything to win his kids over. This too often includes trying to act maternal and loving. And for a child or adult child in a loyalty bind-sensing that liking stepmom is a betrayal of mom-stepmom's overreaching and attempts "to act like she's my mom" will seem especially offensive and threatening. Thus she will be more roundly rejected.

What makes it harder for a stepchild to accept a stepmother? What builds a stepchild's resentment of "dad's new wife"? If you think it's her own wickedness of just plain lack of trying, guess again. It may have more to do with the children's mother than anything the stepmother is doing or not doing.

Based on her 30-year Virginia Longitudinal Study of life post-divorce, Hetherington concludes that stepmothers are frequently singled out for very bad treatment indeed by stepchildren who pick up on their mother's anger and resentment and become her proxy in their father's household.

Dad's house may become the "no rules" household-meaning there are few rules about treating stepmom with respect, both because he is fearful of alienating his kids, and because of his ex-wife’s influence. When a wife or partner with stepchildren attempts to assert her right to being treated fairly in the household under these conditions, her husband or partner may not support her position. This causes tension within the couple, tension which the stepmother may attribute to the stepchildren alone. And so the tension between stepmother and stepchild is further fueled.”

SO, yes, you can try everything under the sun to bond with your stepchild and you MAY succeed, through luck or happenstance or having a heavily supportive DH and/or BM.  However, no matter what you do, you may not succeed.  You could try for years every so-called common sense trick in the book and still wind up being Evil SM, because of the above dynamics that very few want to admit to; or, because the common take on tensions between stepmothers and stepchildren in our culture is, of course, that stepmothers are overwhelmingly likely to be nasty, petty, and jealous, creatures right out of the Brothers Grimm. It would only follow, this cultural logic goes, that their stepkids dislike and reject them.

The problem isn’t with SMs/ SPs anywhere near as much as the problem is with our society’s take on them.  Common sense often doesn’t work in Step World, and many a time, it can even follow backwards.  To just say being a SP can be difficult but rewarding isn’t getting at the truth and minimizes the height of the deck a SM can have stacked against her long before she even says, “I do.”  Of course, a SM needs to be patient and give it time, to a degree.  But, never forget manipulative, controlling BM and weak, enabling DH = Step Hell.  Decide what you can tolerate, and once that line has been crossed, put away your SM card and whip out your wife card, and play it to the max.  You are your DH’s wife first and foremost and not your DH’s housemaid and babysitter.  And, be on the look out for gaslighting.  Trust me, everyone will be trying to make it look like YOU are THE one to blame no matter what.  You need to do your research and know better.