You need an attorney quickly to put orders in place. I can see no reason thaat he would be granted custody over you, but we have not had a thorough conference about all the facts.
I always worry about a non-citizen taking a baby out of the country when there are no orders in place. There are great lawyers in Austin, many of them on this site. Click on the Find a lawyer tab and see what you can find.
Any communication through the AVVO site with Sherrie Travers or any individual member of the firm, Travers & Travers, does NOT establish an attorney-client relationship. Any information given by Sherrie Travers or by any individual member of the firm through the AVVO site is general information and should not be relied on as legal advice. This answer is based upon limited information and is not intended to be conclusive in your circumstances as there may be other factors that might change or alter the advice given herein. Confidential or time-sensitive information should be conducted in person with an attorney.
You need to get a lawyer ASAP.
To directly answer your question. Yes, a non-citizen can be given custody. He doesn't loose rights as a parent just because he is an alien.
Your custody case is the same as any other. As the mom , with what sounds like a stable life, you are likely to be named the "home parent."
There is the concern about removal from the country. I recommend acting quickly to get orders in place.
You should hire a lawyer.
Citizenship is not really a factor in custody, but the other things you mention - stability, good job, etc. - are considered. Your ex will probably be ordered to pay child support and given a visitation schedule.
This answer DOES NOT establish an attorney-client relationship. This answer is based on the limited information provided and is not intended to be conclusive advice. There are likely other factors that might influence or change the advice after a more lengthy consultation.
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