Muzzle training tends to take a little longer than the desired reprieve might be. Generally you want to do this over a couple of weeks so the dog has ample time to adjust to the muzzle and not be scared of it - the association is with treats and praise and not with punishment.
While you're waiting for whatever you decide to do, I really encourage having controlled time with your kids. They see the puppy in a gated area or playpen where, when the puppy bites because they're a tiny Velociraptor, you then remove ALL interaction until they calm down. Walk away, leave them to their own devices (I used to do a 5 min timeout) and then reintroduce. DO THIS FOR EVERY OFFENSE WITH BITING. It helps INSANELY well, these dogs are brilliant and will make the connection that being bitey = no attention at all.
In a similar vein, never flail your hands or try to push them away when they are getting feisty. Your hands and arms are like wacky inflatable men chews toys because they're fun and waving around and they're awesome to chase. So tuck them firmly behind your back, get up, and let them redirect onto something else.
As for the muzzle, I bought an 8 pack of nuzzles that started at size 1 and went all the way to size 8. This gave us lots of sizes to work with since Chase was growing out of them fast. It cost about $30 CAD on Amazon.
The first week, Chase's only task was to touch the muzzle when presented with it. No matter how many times it was presented, he got a treat for bopping his nose to it or sniffing it. Investigation was encouraged.
Second week I would touch it to his face, and for every time he let that happen or moved to touch it himself, he got a treat. Slowly I worked this into holding a treat at the end of the snout so he'd put his head in and grab it. Total time was roughly a week and a half.
Then we moved onto keeping his head in while he ate the treat. After he was comfortable doing that after a few days, I would fasten it and LOVE BOMB. All the praise, all the kisses and love, here's some treats, and then take it off.
The end result of all of this is Chase puts his head willingly in his muzzle when I present it, and he is not at all daunted by it. It's actually the only thing that calms him down enough to cut his nails! Otherwise it's a long, arduous game of hide the paws.