My first solution after the failed clips was to buy a pair of stretchy fuzzy adult sized socks and use them as mittens. The heel stretches to just the right place and it fits perfectly at his elbow. I slid the "mittens" on over his hands and up over his sleeves to the upper arm, then put his winter jacket on. Bonus - the winter jacket slides over the sleeves without the sleeves riding up! And he was not able to pull these off! Even though he didn't have a "spot" for his thumb, he had enough dexterity he could pick up and hold onto things thanks to the stretchiness of the fabric. He has such tiny little hands that are finally big enough he can wear now wear tiny little gloves. But I knew he'd pull these off too . . . so I took the socks-for-mittens idea a little further.
Please note, this tutorial is for mittens/gloves for smaller children. For bigger kids, I'd recommend the taller adult sized fuzzy socks and cut the socks off at the ankle above the heel rather than at the toe seam.
How to lengthen children's gloves (or mittens) :
You start out with a pair of stretchy children's gloves and a pair of adult sized fuzzy socks. First thing you need to do is turn the socks inside out and cut off the toes at the seam:
Place the sock so the heel is on the underside.
Insert the right-side-out glove into the inside-out sock, fingers first. You want to make sure the sides of the sock match up with the sides of the glove so the heel stays in position for the elbow.
Once you have the glove in far enough and the edges meet up, stretch out the edges and pin the glove and sock together.
8 pins does the job.
Hold it so it's stretched and sew the edges together using a zigzag stitch so it stays stretchy after it's sewn.
It should look like this when sewn:
Now, flip the sock right-side out. They are stretchy enough as a finished item that you can easily get them onto a (cooperating) child's hands and get their fingers positioned into the gloves. (Top and bottom view)
It doesn't matter which direction you start the first one, of course, but remember when pinning the second one to put the glove in the opposite position . . . unlike what I did at first because I didn't pay enough attention and ended up with two exactly the same . . . and had to rip the seam out and start over on that one! You can also find adult fuzzy socks without a heel and just eliminate that issue. :)