Hello, and welcome to the forum!
I think yours is a valid concern--at his age, he can jump out of your grasp and run under furniture, etc...not good. A jump from any height onto hard floor would possibly injure him, and one of the kids could accidentally step on him. bye-bye, beardie! ? Actually, I do have some hopefully helpful suggestions.
I taught children in a wildlife sanctuary, where I worked. I brought out all kinds of animals, most of them wildlife that had been injured and could not be released. With small, squirmy critters, I had some tricks to make it safer for them:
First, before removing animal from viv, have the kids sit down cross legged, hands in laps, and practice their "lizard manners". (I called it animal manners) The Idea is to keep the energy level calm and quiet. The "manners" I taught included--no loud sounds, laughter or squealing, because animals think those are threats. We practiced our critter(lizard)voice--just above a whisper. If a child forgot and talked loudly, I would make an exaggerated response by covering my mouth and saying, "oh, no! You just scared me because I am just a little critter, and your voice was soooo big!" Also, no fast movement. (kids loved practicing slow motion moving, and we had fun with that) Remain seated, hands in lap, unless it is their turn to pet it, until animal is back in its cage. Soft hands to pet the critter. very gentle. No pointing, because animals do not use their arms that way, unless they are predators and want to eat what they are moving toward...no grabbing, because predators grab at what they will eat. (I pretended to be a predator, and made a mean face, grabbed at a child.) I also used this as an opportunity to teach what a predator was. We would sit a moment, minding our animal manners. This was fun! Many of the kids were very serious about protecting the animal, and they would not move while he was out. Super cute.
Now, we are ready to bring out critter. I sat also cross legged, keeping animal low so it would not be injured if it did jump, and held critter with both hands--one hand gently but firmly around the chest under the arms, one hand near the pelvic bones.This gave me better control, and if animal struggled, he would not hurt himself. Usually, they did not struggle because they felt secure. I always held the animal myself as children could get excited, unless one child was exceptionally calm and seemed to take the safety of the animal very seriously. Even then, I kept one hand on critter, just in case. We always reviewed our critter manners for a moment, even if the kids had been there before, with them telling me what they remembered. These measures kept the energy level low, and the animals stayed calm and both children and animal enjoyed the experience. If one of the children started to move around or forgot their manners, it was time to put away the animal.
For particullarly squirmy animals, I had a large plastic bin (from the dollar store or Walmart) that I placed in front of me, and held the animal over that, ao if it jumped, it would jump into the bin. I could easily retrieve animal from the bin because the slick sides and floor of the bin slowed down escape attempts.
. Another idea is to bring him into the bathroom for his social sessions. Everyone can sit cross legged on the floor, as described.. The children can then see him and pet him, and you can control the situation better. With the door shut, if he does get loose accidentally, you can have the kids wait outside the door while you pick him back up. (an added bonus is that Beardies cannot run as well on a slick surface like vinyl floors!)
Sorry this is so long..I hope it helps. When your Beardie is older, around 6-8 months, he will settle down and become much more relaxed and laid back. Then the kids will be able to hold him on their laps! I commend you for taking preventive precautions, and not waiting for the distaster to occur!
Dezi says, you are a good lizard mom!