If your husband accepts your 6 year old, really it's time his mother tried a bit harder I feel. I do understand her feeling excited now that her son is a father - but he was a father before that when he took on the fatherly role for your daughter.
Did she visit at that point? Did she try to build a relationship with your little girl? You say "mother-in-law and family" - who else wants the baby? Is it your husband's siblings?
If I was you I would find it quite hurtful that your mother-in-law seems to be cutting your daughter out. She needs to spend time with you as a family I think. Not just with her new grandson.
But, please don't save all your family time for your parents either, share it about a bit. Do, of course, also make time to grow strong as a family team, and spend time together as a family of four too.
Because of the need to reinforce the idea of your family, I think I'd want to visit her as a family^. Continue inviting her to your house but don't allow yourself to get stressed if she doesn't come. Maybe suggest your husband calls her to ask her to, say, join you four for a picnic - perhaps she will find it harder to be rude to him.
And yes, as others have said, ask him to please support you and not make you out to be a person who needs convincing.
Finally, you have been pumping milk for your baby for months. What a relief to be able to stop this. Enjoy your time with your little family free of the constraints that pumping brings. Don't let this be spoiled by people outside your family whoever's they are. Keep offering to share your days with her, but don't think you are a bad person for feeling that you want to be with your son. You cannot help the way you feel and only you know what you are feeling deep inside. I am sure you have done the right thing in giving up work if you can manage financially. In 50 years time you will not look back and say "goodness, I wish I'd worked more and spent less time with my children". The early years fly by and soon your daughter will be at school and the dynamics will change again anyway.
I do hope you are able to resolve this soon. And I do hope your husband helps you do this.
Good luck.