I'm a stepmom with 2 stepkids and 1 with my husband. I know how hard your situation is! It's okay for him to do things with his first set of kids now and then, especially because they are older than your kids. However, he is lying to you and sneaking around, and so this situation is totally unacceptable.
In my view, he should be going to things like doctor appointments and teacher conferences with his ex and without you, since you do not have a say in these things. But he should not be leaving you out of public events like graduations, performances, athletic events, etc. He should be sitting with you and not his ex if he's uncomfortable or if your presence bothers her. If he is sheltering his ex-wife, or if your stepkids are worried about your presence upsetting their mom, then that needs to get verbalized, acknowledged, and worked on. The kids' birthdays should be celebrated twice - once with their mom and a second time with you and your husband.
If you have little children, they should be attending events according to the situation - they should not be going to plays and concerts (no fun for them or for you who has to watch them - distracting to the older kids). Outdoor athletic events might be something your little kids could attend. In any case, if you are there, you should be able to focus on the stepkids and let them know they are important to you.
Your husband's behavior is demeaning you, and it sets a bad example for all of the kids. If his kids don't like you, then he's letting them run the show, which is not acceptable. He may have some guilt about "abandoning" them but he's just reinforcing it by keeping you out of their lives. They have half-siblings they are entitled to know, and whom they will benefit from knowing. His children will have an opportunity to see their dad as a good father to younger children which will reinforce their opinion of him. Abandoning YOU and your kids just makes him seem like a sleaze in the eyes of the older kids. "Oh, he abandoned us, then he started a new family, and he leaves them alone to see us." Right now, they might be enjoying the attention, but ultimately it doesn't make him seem like a good guy in anyone's eyes.
The biggest issue is the deception. You're got to get into some couples counseling right away. Your medical insurance might cover a number of visits - ask your doctor or clergy person for a referral. Low cost counseling is usually available thru your town's office for children's & family services, or other resources. Start asking for referrals right away. Stop talking to him about what he does - since it's not sinking in. If he won't go to counseling with you, go without him to start. You need to have some strategies to deal with him.
Good luck.