I am making a leather wall hanging....with leather embroidered blocks. the gray leather sashing is a bit thicker than the leather embroidered blocks. while trying to stitch them together, i was having problems with the thinner piece stretching. i sewed and unsewed several times before i came up with a solution.
I cut about 1/2 inch strips of lightweight fusible stabilizer and ironed it to the back edges of the embroidered blocks. problem solved. no more stretching.
And, yes, you can iron on the leather. i put a pressing sheet on top of it first. just pressed enough to hold the stabilizer on.
That's all I got...carry on.