You asked two different questions, but the answers are similar.
(1) Can a registered sex offender be around his own child? Unless there are orders in place saying otherwise or putting conditions on being with the child, yes.
(2) Can a registered sex offender live in the same house with his niece and her parents? Again, unless there are orders saying otherwise, yes.
If either child has been the subject of a SACR/Divorce, there should be language in the final decree saying that if a parent lives with a registered sex offender, that parent has to notify the other parent/conservator. That may not apply in your case.
A comprehensive web site on Texas sex offender laws is here: http://www.dshs.state.tx.us/csot/csot_solaws.shtm
There are federal laws as well, but the Texas law are more strict.