Now... I'm responding after your update, so this may be a bit different from some of the early posts. I'm seeing a NUMBER of different issues going on, and I'm going to try and hit most of them:
1) I think you're focusing a lot on "blame". NO it's not your fault that you were not in your biological niece's life as a child or young adult. Absolutely NOT your fault, doesn't reflect on you, you weren't some uncaring absent aunt. HOWEVER... that doesn't change the fact that you weren't in her life. You came into her life when she was already an adult. That's just how it is, and it doesn't matter how/why, the results are the same. You weren't there in any way/ shape/ or form when she was growing up. You were a complete stranger to her when you two met after she was already grown.
2) She has her own family. You are her BIOLOGICAL aunt, but she has her own parents, aunts, uncles, grandparents, cousins, nieces, nephews, etc., in her adopted family. Just because she was adopted, does not in any way lessen her family obligations nor relationships to her adopted family. They were the ones who raised her. They are her parents, her family. Plus, having a child, chances are better than even that she has inlaws / her husbands family that she has married into. BOTH sets of families, her own and her husbands are going to be higher priority to her than her biological extended family that she didn't meet until she was an adult IF she actually is well adjusted. Her own family is going to be the priority in her life. As it should be.
3) She has her own friends. Friends from childhood, college, work. People she's spent years fostering and developing relationships.
4) She's a young mother (being defined as any mother with children under the age of 2). Young mothers, in my life, get a 'free pass'. Sleep dep alone, but coupled into aaaaaaaaaall the other challenges means she has VERY limited time. Relationships, both deep and of long standing, often suffer or at the very least go into "starvation mode" with young families. Trying to juggle your own is hard enough, trying to balance in both your own parents and your husbands, much less your siblings, his, grandparents, aunts, uncles, cousins, friends... it takes YEARS for most families to be able to get the "balance" right between their own family and the families they came from (parents, etc.), and their friends, and colleagues. Adding in that your biological niece has TWO families (adopted, and birth family that she has only recently started to reconnect with) doesn't LESSEN the juggling. That she's trying to "fit you in at all" shows that she really does care to, and is probably going to great lengths to.
5) You were an ADULT (I'm assuming, if not skip to 5.5) when she was a child. This has 2 bearings.
- 1, YOU were closer to her, than she was with you/ actually have memories of her when she was a baby/very small.
- And 2, even if you have a young family of your own, you've had and extra FIFTEEN - TWENTY plus or more years of life experience on her. You've learned lessons she doesn't even know exist, yet. If they are OVER the age of two, you've also figured out your own juggling/ get decent sleep on a regular basis. But it seems as if your expectations on her are that of either a close relative, or a close friend. YOU may feel the bond, having known her as a child, but to her, you are an utter stranger that she has met a few times.
5.5) If you were NOT an adult, or at least a teenager, but a "child aunt".. if she had grown up with you, your relationship would still be completely "non-aunt". More like cousins. Since you didn't grow up together, you're "just" another peer. Learning the same lessons, trying to figure things out Like running into someone you knew in kindergarten who moved away. But again, it seems you are holding her to a position as if you two *had* grown up with each other and have that relationship. It sounds as if you want her to fulfill your idea of "x" role.
6) Families do things differently, have different priorities, view roles differently. My own family doesn't send christmas cards or birthday cards. Ever. Instead we have our own traditions. We call and we come on extended visits and catch up. Voice to voice, or in person. Card are considered impersonal and impractical. Not sending a card isn't "slighting" someone. Not CALLING is. But in other families, it's the cards that are important, not phonecalls or visits. In some families complimenting a child is bad luck. In others, not doing so is bad manners. In some families, in others, in some families, in others. Your biological niece was raised in an entirely different family with their own traditions and protocols, but you're holding her to the traditions and protocols of your own family. Insisting, subconsciously or purposefully, that she follow "your" rules / family politics of interaction. She wasn't raised in your family. She's going to follow different rules.
7) Individuals are different. Meaning, even in close families not everyone likes everyone else, and there are different degrees of closeness. Some people pure and simple, don't like children. They love their own, but they aren't "kid people" or "baby people". They can be fantastic parents, but they don't get on well with other people's children. Other people CAN be kid people but completely and totally disagree / have different parenting styles than other people (you see those Q's here on this board all the time, trying to come to some sort of balance with people they like/love but parent in totally different ways). KIDS are also all different from each other (and we already know that your and her parenting methods are quite different, as well as your children and how they react to situations; from your kids mobbing up on hers, and her asking for space, and you getting upset about that). ALL of this adds up to longterm relationships distancing or dissolving. Or new relationships not starting at all. Would you be friends with her if you met her in the park? Would she be friends with you?
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What I'm hearing is that you loved your niece very much as a child, but now that she's trying to reconnect with her birth family, you are taking none of the past 20 years into consideration. You want her to follow your family rules, devote as much time and effort into the relationship as if she'd never left the family and been raised by another. If you take into consideration the past 20 years, I think your biological niece is being incredibly brave and pouring a ton of effort in trying to reestablish any kind of relationship with her biological family at all. I'm hearing that you have a lot of expectations on HOW she "should" be doing this, and "who" she is "supposed" to be... instead of just getting to know her for who she is, and recognizing the huge amount of effort she's putting into even having any contact with you or her other biological relatives. Also not taking into consideration that she is doing so at a time when she has so much going on with her own life, and is well within reason and her own rights, to not pursue any kind of relationship whatsoever.