Without knowing more facts I cannot give you your chances, but I can tell you what the courts look for in gaining or providing custody. First of all, they DO NOT look at adultery or extra-marital affairs. While in the past that would be deemed a possible claim to providing evidence that the other party is morally unfit to raise the children, today that is no longer looked upon. What the courts look at, instead, is what they deem to be "in the best interest" of the children as well as the fitness of parents. Fitness is looked upon as possible history of abuse, neglect, domestic violence, drug use, alcohol abuse, mental illness, criminal record/history/parole/probation, & moral turpitude. The courts also tend to favor parents who wish to reside in the current location, and those that have a proper home for child-rearing.
For you to prevail you must show the other parent as unfit. Possibly using her late-night trips and lack of attention towards the kids as "neglect", and claim that since the children have a stronger bond with you, you should be granted a bigger role in the raising of the child. The home, on the other hand, is usually granted to the party in whose name the home is listed. If in both, you can request it, but she does not have to comply.
DISCLAIMER: Answers from Experts on JustAnswer are not substitutes for the advice of an attorney. JustAnswer is a public forum and questions and responses are not private or confidential or protected by the attorney-client privilege. The Expert above is not your attorney, and the response above is not legal advice. You should not read this response to propose specific action or address specific circumstances, but only to give you a sense of general principles of law that might affect the situation you describe. Application of these general principles to particular circumstances must be done by a lawyer who has spoken with you in confidence, learned all relevant information, and explored various options. Before acting on these general principles, you should hire a lawyer licensed to practice law in the jurisdiction to which your question pertains.
The responses above are from individual Experts, not JustAnswer. The site and services are provided “as is”. To view the verified credential of an Expert, click on the “Verified” symbol in the Expert’s profile. This site is not for emergency questions which should be directed immediately by telephone or in-person to qualified professionals. Please carefully read the Terms of Service (last updated February 8, 2012).