Per your post yesterday, you are posting your question in the wrong category. I'm just trying to save you time by pointing you in the right direction. Since it is your brother-in-law's house & his phone, he is not committing a crime such that you have a remedy in Family Court. Once again, you're encouraged to re-post your question in the Elder Law category to see if there's a remedy there.
Unless there's domestic violence (or something close to is), then usually no one needs to leave while the divorce is being worked out. If you own the house, it will generally be sold, so at that point you'll both need to move. As for "working things out," you may approach her with the idea of counseling or mediation, but that's voluntary on her part. Schedule a consultation with a NYC Divorce attorney for a full assessment.
It really depends on what the visitation order says. If the order says "8pm drop-off," then Mom's arguably violated it. But rather than cause more issues with a violation case, I suggest your Dad try either speaking to her or writing to her and point out the discrepancy and ask to revert to the order. If she refuses, then your Dad will need to file a violation petition.
Yes - having temporary custody is indeed a factor the Judge will consider at the ultimate custody trial. This is because stability in the child's life is a specific factor which must be weighed. That said, there are numerous other factors which must be considered as well. For a full assessment, you're best advised to schedule a consultation with a NYC Child Custody lawyer.
There's not really anything you can do in advance because he would need to be served with a summons & if he's not in the country, you can't serve him. That said, upon his return, if he files, you may counter-file for an order of protection (if warranted) and a request that his visitation be supervised. Nevertheless, for a full assessment, please schedule a consultation with a NYC Child Custody attorney.
So long as the server in his/her affidavit of attempted service was able to verify that was indeed her residence, then you can file an application for substituted service. Attached the affidavit as an exhibit to the motion. The Court will usually approve affix-and-mail service under these circumstances. Schedule a consult with a NYC Divorce attorney for a full assessment.
Preliminarily, I'm concerned that you executed a "settlement agreement" but no case is actually pending yet. Usually, one "settles" a case which has been filed. In any event, whether the agreement is valid & enforceable depends on what it says. This, you'd need to take it to an attorney for a review of same. As such, call a NYC Divorce attorney to schedule a consultation.
You can sue him for child support, assuming the child is his. That said, I doubt you'd have any claim for breach of contract due to the lack of any "bargained-for exchange of things of value." Moreover, any emotional distress would have to be more than merely getting upset - it would need to be a serious psychological conditional attested to by your mental health professional and linked to the incident (i.e., an extremely hard burden to prove). If you're interested in suing for child support,...
Yes, you're highly advised to have it reviewed by an independent attorney. While a mediator may see things one way, an attorney who's on "your side" may give you different advise. As such, schedule a consultation with a Putnum/Westchester Divorce attorney for a full review & assessment.