Herd won't stay in pasture - any suggestions?

Hi all, I have two sheep and four goats that live together. I have spoiled them with attention and they love being scratched and petted. The problem is, they hang out all day in the barn - seemingly waiting for me to come give them some attention or food. They have a perfectly good pasture - but will only go out into it when I go with them. If I am out there in the pasture with them all, they act like they have been given a Christmas present, eating plants and brush with a vengeance, but just until I start to leave - then they panic and want to get back to the barn. I tried fencing off the barnyard so they have to stay in the pasture, but they cry out and work at the fence until they find a way to break through and run back 'home'.
Any suggestions?

Everyone following me around.

This is where they are ... all day. I am having to clean out their bedding so often!

Everyone wants to get their head scratched!

Maybe I am mean, but if there truly is a lot to eat in the pasture I would try not giving them free choice hay (unless someone is pregnant or you have kid). Mine get lazy sometimes, so I give them a little in the morning and then fill the feeder in the afternoon.

Remove whatever feed you are giving them in barn. Either stop feeding it entirely, move it out to the pasture, or, if you are bringing them to the barn at night, save the hay for night feeding.

Try putting their grain dishes out in the pasture and start giving taking them out and giving their grain out there. As soon as the feed is down, walk away while they are busy.

We have had high heat here and all our goats are staying in the barn under the fans. They will come out if we go in the field but then once we leave they are right back.

@purplequeenvt has great advice so if not the heat then take away their incentive.

One other thought. We have LGD's and the goats know they are safe and protected. If your goats are scared because they know something is out there, they may feel safer in the shed... or when you are there.

I was coming back to say basically what @Southern by choice said. Maybe if they had a covered area in the pasture that felt safer? Then maybe they would get brave and venture out. Especially if they run out of hay!

2X all the above. Don't know when the pic of them outside was taken but, the pasture is sparse for those animals in that particular area. If all of their field is like that I would definitely put a few pads of hay outside....a fair distance from the shed. NO ONE looks underfed, that isn't my point -- simply that goats eat a LOT of roughage. When nothing to munch on, they laze around. Maybe some boxes, ramps to play on? I think they are looking for something to do and YOU are it. Maybe expand their attention. Well, goats anyway.....I think sheep are different.

They were in the yard in the picture, pasture land looks like this:

I am going to try all of your suggestions, and I'll let you know how it turns out!

BTW- Beautiful little herd/flock you have there!

Thank you!