Hello. My name is Marc. I'm a licensed attorney and I will be happy to answer your question. I'm sorry this happened, and I can imagine how anxious you must feel for your granddaughter's safety after such an intrusion. The short answer to you question is yes- you have a right to sue the property owner and/or management company. The real question is on what grounds and whether such an action would succeed.
In Texas, landlords have a legal duty to keep rental premises livable under a legal doctrine called the "implied warranty of habitability." If a landlord doesn't take care of important repairs, such as a broken heater, tenants in Texas may have several options, including suing for any damages that result from the landlord's breach of the implied warranty of habitability.
So what does it mean to say that your landlord is expected to fulfill an implied warranty of habitability? It means many things. The list is long, so I won't go into everything here. Pertinent to your case is that the landlord is expected to keep basic structural elements of the building safe and intact and provide rental property that is reasonably safe from the threat of foreseeable criminal intrusions.
I don't know the details of how/why/where the break-in occurred in your case. But, if you can imagine some way in which the break-in was enabled by some failure on the part of the landlord, you would have grounds to sue for negligence and breach of implied warranty of habitability. For instance, if you learned that the front gate had been left open and unmonitored, that could have been a negligent act by the landlord which allowed the burglar into the community. Perhaps the security guard was asleep or too busy playing games on his iPhone (not uncommon!). Or, perhaps the locks, doors or windows in your unit were defective or broken and, despite having notified the landlord, they were never repaired.
By contrast, any action against the owner would not be successful if the break-in occurred as a result of acts or forces beyond the owners control. For example, the owner would not be responsible if a clever burglar climbed over a fence in the middle of the night and quietly broke in. The essential question is whether the circumstances of the break-in were reasonably foreseeable and whether the property owner took reasonable measures to secure the property.
You should contact the police if you haven't done so already. Following their investigation, you can ask them for their findings and determine whether the owner should be held accountable based on the above standards. You'll also want to notify your insurance carrier, if any. So, let the police do their job and see what they come up with. They will most likely not make any determinations as to whether the owner was responsible, but they will find the facts you need to make that determination for yourself. Also, consider asking around and conducting your own investigation.
If you determine that there's something that the owner did or failed to do and that but for that act or omission the break-in would not have occurred, you should consider retaining an attorney to pursue the matter for you. In particular, you would want reimbursement for the stolen items AND you would want to force the owner to take necessary precautions to keep the premises and your granddaughter safe.
I hope I have answered your question and provided useful information to help you better understand your issues and options. If so, please rate my answer, since that is the only way I can receive credit.
Meanwhile, I wish you luck and a speedy resolution to this matter.