Your patch sticking is caused by a number of reasons. First lets make sure we are on the same track. You are using a jag head to work the patch I am sure. Some people use a patch worm, I do not.

Make sure the patch is not too large or too thick. I buy these cheap pre-cut patches at Wal Mart (since I ran out of old socks). Sometimes if the patch is too long cut it in half. A 2-2.5" circle or square is all you need.

I make my swab solution. I use 50/50 isopropyl alcohol and car windshield washer fluid. I soak the patch good at first then ring it out a little. Set it over the muzzle and then push the jag into it instead of wrapping it around the jag head.

Start at the top and work the damp/soaked patch SLOW up and down the barrel about three inches at a time. Then keep increasing the amount you travel in the barrel in three inch amounts, working all the way down to the breech with the first patch.

Since it sounds like your bore is tight, I would then run a second damp patch all the way down now and back up. This is when you need to run a bone dry patch to the bottom of the breech and back up. It does not hurt to run the three inchs at a time rule here. If it feels like it is getting stuck do not go further. Pull it out.

Last is get a T-handle for the ramrod. The extra power a T-handle gives you is amazing. If you do get stuck, sit in a chair, put the T-between your feet with your knees bent, hold on to the rifle then push with your legs straight away from the rifle and the ramrod and patch will come out.....

Your second shot should load easier then the first shot because sometimes that slight fowling left in the barrel acts as a slide of types and makes it go down better. That does not mean you should not swab between every shot on the range.

For hunting, experiment. Find a sabot or conical that will load fast and easy for the second shot without swabbing, should you wound an animal and it is trying to get back up and you need a fast second shot. A powerbelt or maxiball or maxi hunter works here. So do minnie balls. They are a slip fit conical..

If you shot and that animal takes off out of sight, the second shot speed is not important. Take your time. I carry a small spray bottle that held eye glass cleaner with my swab solutuion and some patches, in my possible bag. I can then swab the barrel, calm down, load my second shot carefully and correctly, and give the animal I wounded a chance to lay down and expire.