P.W.
I don't blame you for feeling hurt that your son was not included in the wedding, but let it go. They don't get it yet because they don't have kids. Go with it and be understanding.
Your mother-in-law........ well, no one is perfect. Talk to your husband about what you both are comfortable paying her and just pay her when she babysits. Treat that like any other babysitter. If you can't afford it then don't have her babysit, and explain it to her. But when you are willing to pay, pay her, not someone else. This will be hard for her to accept since you take family, vacations, etc... but you don't have to explain. Everyone spends and saves differently. it may bug you, but all the kids know is that grandma is coming over... and you want to keep it that way.
Invite your husbands family to your house. Include them and their kids. When opportunity arises tell them you would like to see them more but it's hard for you to leave the kids out. Invite your mother in law for dinner for no reason. Possibly on a weekly basis. Let Monday's be Grandma night for example. You can endure her for a couple of hours and it may just make her feel you care about her and go a long way to mend fences. If once a week sounds too much then at least try to do it monthly.
In counseling be open and tell the truth. Let the counselor help you and your husband find a middle ground. Tell your husband if you feel abandoned. It sounds to me like you are telling him to go, but then you resent when he does. Talk about that and work it out. Admit to yourself the problem is never one sided and you both have to be open and honest to get through it. If your husband is willing to go to counseling then he is a keeper. Do your best to find that middle ground and accept his family as much as you can.
I'm not saying you don't have a right to be hurt and that there is no reason for your angst, but what good is it doing to hold the family at arms length. Do your best to embrace them. If they are jealous that is their problem. Try not worry about it, but for your husband and children try to make a go of it. Maybe you should have a family picture taken at your house........with YOU in it! Show them you want to be part of their family.
Last, talk to your counselor about limits. You want to embrace your in-laws, but that doesn't mean they should take over your lives. Your husband needs to do his part and let go of them a little bit too. Write it all down and talk to that counselor!