I'm a father of three kids with my ex wife. She dumped me after 11yrs when she found out my buddy had lots of money and a big house. Court realized I was a good father and gave me 50% custody. I paid no child support or alimony. When the kids were with me for a week I'd pay for them, when they were with her, she'd pay for them. Of course they were spoiled by a guy who would buy them lots of things so they would get lost so he and my selfish ex would have more time to themselves. I didn't have a money tree and even if I did I would have stayed the course that I did being a father first and foremost. My kids have come to realize the jerk their mother can be and the jerk the guy was. (yes, he died at 50yrs!) Sorry, can't say I was broke up.
With the whole experience I learned to document everything I did with the kids and everything the ex with Mr. Wonderful did with the kids. I never tried to compete with them and always did the right thing. You need to do the same. Don't "buy" your stepson's affection or respect, earn it being a good dad. Don't diss his POS biological father as they don't want to hear it. Sometimes it's hard but keep in in the back of your mind not to do it. My kids are now a lot older. My son, the youngest, (23) keeps telling me time and time again how much he realizes how his mom and his deceased step dad tried to buy him and how it worked for a while. My oldest daughter says and knows the same yet has some issues of her own she needs to work out. My middle daughter choose not to have a relationship with me since she was 14 because her mom "bought" her affection by giving her everything she wanted including letting her go out with 20+yr old guys when she was just 14! My son now tells me his sister has started showing regrets that we don't have a relationship and acknowledges that it is her who is to blame. There is hope that she will come around but she has grown to be even more selfish than her mom.
The one thing I can say is I acted honorably like a dad and role model should all through the years. I can hold my head high and know I never stooped to kids games or revenge to make myself feel better. Just continue to take your stepson shooting and progress up with the weapons like your normally would. His day of shooting his first cartridge gun has passed. He will have many more firsts with you and they should be "normal" firsts.
Remember, if you do have a family day with the wife's ex make sure you take lots of pictures. If it ever comes up in court for any reason you have proof that he agreed to do it with you.