You're not coming across well here. It looks like foot stamping and sulking and not-fair-ing , and it's all about what you and your family want instead of what's best for the baby.
You refuse to take friends and family to the home of your baby and your ex-partner because you feel uncomfortable there. Yet you are demanding that your ex must bring the baby into a household where she feels uncomfortable and unwanted, for the baby to be passed around 10 people at a time. Can you really not see the irony here ? You are seeing your arse because your ex won't do something that you have refused to do. At best you appear petulant ; at worst, controlling.
By the way, seeing people in your own home is not the same as seeing visitors in your own home. As you weren't involved in the actual birth and subsequent recovery, you have been shielded from the physical realities facing your ex. She might well still be bleeding heavily, and not want to have to change pads and clothing in your mother's house with 10 people all wanting to use the bathroom. She might be recovering from painful tearing around her vagina, or have piles, or still recovering from a c-section if she had one - if so the thought of having to stand or sit on the floor for hours might be worrying her. We don't know how long the baby has been bottle fed, or whether that's exclusive - your ex might well have painful and leaking breasts. She is almost certainly exhausted from lack of sleep. She quite possibly finds it very difficult to cope with any separation from her baby - many women have a physical reaction to being apart from their newborn, even when the baby is with a trusted relative. And that is due to hormones - evolution has ensured that new mothers have a strong urge to protect their child above all else. With this in mind , don't you think it's reasonable to understand that having to cope with all this when feeling unwelcome in a potentially intimidating household might be too much for your ex ?
Your best bet might be to suggest that you gradually introduce your family and friends to the baby , either in the baby's home or in a neutral environment like a cafe or restaurant. There's no reason why everyone in your family has to meet the baby at the same time on your turf ( unless you were hoping for some kind of hero-worship party where all your family and friends are on hand to admire your masculinity).
It's great that you want to build a relationship with your child, and that you are happy to be a supportive father. Please don't undo all your gpod work by being unreasonably demanding now.