The TSA Can I Bring?, impressively, has entries for both Balloons (inflated) and Balloon (uninflated).
For Balloon (inflated) it says:
You may transport this items in carry-on or checked baggage. For items you wish to carry on, you should check with the airline to ensure that the item will fit in the overhead bin or underneath the seat of the airplane.
So airport security won't stop you. I can see the airline having some concerns however - one is that a bouqet of balloons is probably bigger than your carry-on allowance, especially if your mother is attempting to take carry on luggage as well. Of course, some airlines largley ignore these rules.
The other concern may be about the balloons popping and disrupting other passengers as the cabin pressure drops. You mention "lighter than air" in your question though, implying these are probably helium-filled balloons. If they are of the "foil" type, then I imagine those are a bit stronger. If plastic/latex, then the pressure change may just cause a faster leak rate than normal, rather than popping.
Anyway, it seems your mother shouldn't get in any trouble for trying it - just don't try it if someone at a later point asking to take them away will cause too much upset.
In the event that your mother does take the balloon onboard with her, and is unable/unwilling to stow them in the overhead lockers, she should probably be aware of the somewhat counterintuitive physics of lighter-than-air objects in a moving vehicle, when attempting to keep control of them.