Your life is what it is. You can't change anyone else but you can change yourself. I suggest you stop depending on your boyfriend for doing fun things. Get a driver's license or take public transportation and do things with your kids.
I would not allow myself to get into a relationship such as yours but you're in it now and what are you going to do about it. Either find ways to make yourself and your kids happy within this setting or get out.
I get feeling down, angry, frustrated, jealous. For me this would be an indication I needed to change my life. We can't change everything at once. Choose one aspect and take a good look at it. Going out with the kids would be a good one to start with.
Overall change the way you look at things. Focus on positive thoughts. When you see the brother and his girlfriend and child getting what you want remind yourself that you don't know how they feel about it. Be thankful for what you have.
As for shopping with your mil and "sister in law" call and ask to go. They go every weekend. So next weekend call on Friday night or Saturday morning and ask to go. Do it in a friendly manner and accept the answer gracefully if it's no this time. Don't expect them to know what you want or to even cater to you. Be an independent woman who is able to accept a yes or no without whining or showing disappointment.
Perhaps scope out something that would be fun and invite them to go with you. Invite them to your house for dinner and a movie or playing games. Develop a friendship in which they'll enjoy your company.
I go back to getting out with your kids on your own. I suggest that if you feel less trapped at home you'll be a more fun person to be around because you'll be happier.
I would also get out on my own without the kids. Leave the kids at home and go for a walk, daily, as a starter. Develop interests separate from your family. Develop yourself as a person who doesn't need anyone else to make you happy.
After your SWH: See a doctor and get help with your anxiety. There are many good medications that will help you get control of your anxiety and allow you to start living more comfortably.
Your boyfriend is depressed. Medication would help him too.
And.....counseling would also be a big help. Call the county department of mental health and get in touch with a low cost clinic.