I'm assuming in this context you have no siblings, and so your cousin is your only 'family' of this generation. Because otherwise I can't really see what the really big deal is about staying close to your cousin. (But then again I have loads of cousin, so only keep in touch with the ones who are truly my friends).
So in effect, I'm guessing she is a bit like an older sister, but any potential fall out wouldn't be quite so bad because you have different, albeit related, parents. So I will base my answers a little on that.
My eldest DSis had a real 'mother' thing going. She felt she had the right to do and say whatever she liked to me. She thought she could tell me what to do, that I should be running to her for advice all the time, etc, etc.
But, like you and your cousin, she and I are very different people. She left home when I was 8 years old, so I never really knew her as a sister that lived with us, but rather just visited.
It is only now, in my 40s, that she has finally pulled her head in. Spent most of my 20s and 30s arguing with or ignoring her (didn't live in the same city, so ignoring was relatively easy). It was only because of my parents that we maintained some sort of contact for many of those years.
Being the older one, she would have been used to being the one in control, being the 'bossy boots'. Things matter if SHE decides they matter.
This may change, it may not.
If you want to keep in contact with her, you need to draw a line under what has happened and decide how you want this relationship to proceed.
Clearly you don't want to be at her beck and call.
Arrange a time for her to come and see you, but make sure it's a time when you won't be inconvenienced if she doesn't come (a day when you could plan a picnic in your own garden, etc). If she cancels, it will then only be mildly annoying rather than aggravating.
Pop past her shop one day when it suits you, but only that, pop past on your way elsewhere, so that she knows you've made a bit of an effort and are thinking of what's important to her, but you will do it in a way that fits in with other things in your life (don't rub it in though!!!). The thing is, running your own business is pretty special. Lots of people have children (she has!), but not a lot of people have their own shops. What she has done actually IS out of the ordinary, and would have taken a lot of guts to do.
If she cuts you off or walks away again when you are mid sentence, just laugh and walk away. It's possible that this is her, and she does it to everyone, not just you.
Also, why shouldn't she prioritise friends? Friends are people you have chosen to have in your life, they have also chosen to have YOU in THEIR lives. That's pretty special, actually. You and she don't have a lot in common by the sounds of it, so please don't get upset that she makes more time for her friends. Quite honestly, I think you should start thinking about prioritising YOUR friends as well (a bit of an assumption here, given that you haven't actually said anything about your own friends!).
Friends are the ones who you help out, and will help you out. I'll bet she has had friends help her set up her shop, and bounce the idea of having a shop with. Why should she prioritise you over them? Let's face it, you HAVEN'T even seen the shop, and certainly didn't know anything about it before hand.
Also, babies are cute, for some people. But even my best friend's DD, I love her, and I do love cuddling her every now and then, but bloody hell I'm happy to hand her back and I'm bloody happy that time of my life is over. Babies are hard work, and I just don't have the energy or, TBH, all that much enthusiasm for them. When your children get older you can forget how overwhelming and consuming those early days/months/years are. It's quite nice to have lunch or a coffee without the input interruption of children and hard to put up with it again when your's are older.
Just accept that the relationship needs to be on a different footing, and try to move on on that basis.