I googled "mountain fresh tomatoes" and found a photo of the fruits at a commercial site. They look to be a smooth fruit on a hybrid plant, so my own guess would be your skins may be wrinkling from either overwatering or inconsistent watering. Is that a possibility?

Also, some tomato varieties are bred to have tough skins...less fragile for shipping, used for canned tomato products etc. Picking tomatoes too early and then allowing them to "ripen on the window sill" will often result in tough skins. Skin gets thinner at the end of the ripening (on the vine) process. They also have better/sweeter taste if allowed to fully mature on the plant.

You'll regret it if you don't remove them, sorry. See previous discussions on this linked below. Also, please be sure you are using a tested and safe canning recipe. Many on the net are NOT safe recipes for canning. Use the approved recipe in the Ball Blue Book or the one from NCHFP the National Center for Home Food Processing. There are also many recipes here that a search will pull up. The recommendation for pre-squeezing is so you will have a thicker sauce. It gets rid of much of the water in the fruit up front and can save you lots of time in cooking down the sauce. Dave Here is a link that might be useful: Why remove tomato skins discussions...

Yes, very hot here in southern Colorado..average 100 degree weather the last couple months. I also grow in grow boxes in a greenhouse so even hotter in there though i have it vented and also have a fan on the hotter days. The larger tomatos dont seem to be as effected as the smaller ones.