You will need to review the wording of the decree or other other order that established your boyfriend's rights to visit the children. If the order is silent on the issue then your boyfriend is not in violation of the order. I would urge your boyfriend to seek the advice of a local familly law attorney to address all of his and your concerns on this issue.
The answer will most likely lie in the court orders. If your boyfriend is unsure of his rights, duties, and obligations under the court orders, have him consult with a Texas family law attorney. Most attorneys charge a reasonable flat fee for this service and some will even do it virtually (i.e., via email, video conference, and phone).
As a Belleville, Illinois Divorce and Child Custody Attorney, there would be no problem with watching your boyfriend's kids so long as you watching your boyfriend's kids does not violate the terms and conditions of any custody and/or visitation Orders and/or understandings and so long as there are no disagreements or disputes. If there are disagreements or disputes regarding this, an appropriate Order should be requested from the Court.