I've been a stepmom (and now stepgrandmother!) for over 25 years. You are not "meddling" when you are involved with your stepdaughter, you are necessary and important in her life. You are a parent to her when she is in your home. Yes, her father needs to be the main disciplinarian, but there is no way you can be uninvolved, as you know. Her father should back you up and enforce that she treat you respectfully.
12 year-olds don't say "thank you". I never expected it. She is trying to assert her independence when she says "I bought it". A 12 year-old would be jealous of a baby even if it were her biological parents' baby. Don't take anything she says personally.
Ignore the ex-wife as much as possible. It would be nice if the two of you could cooperate, but it is not essential (NEVER happened in my family). There is very little reason you should even need to talk with her, she can communicate with your husband. You can't stop her from being jealous, but you can stop being involved with her at all.
I'm glad to hear you are going to counseling. A third party can be so useful in getting things out on the table, and coming up with new approaches.
Things I've learned:
Stepparenting can be a thankless role (or it can be very rewarding over time, just not right now :-)
Don't take anything personally.
Step back and look at the bigger picture when things seem overwhelming.