My neighbour called me over to ask how the rabbits were getting along then decided to tell me that she’d be more worried about the foxes than the cats, she preceded to tell me that foxes can climb fences and even if they can’t get into the enclosure my rabbits could die from a heart attack from being scared, I don’t know if she was just being helpful but she’s got me worrying even more now.
I’m thinking it may be safer just to bring them inside the house each night and leave them out in the enclosure during the day, it will be such a shame though they won’t have as much room inside as they would in the new enclosure.
while unhelpful to your worries, she is right. foxes are as much (I personally regard them as more) of a risk as a cat could be. foxes would be out for food and a rabbit is on their diet in terms of prey they'd catch. they may try, which is why its important to fox proof runs etc, such as making sure they can't be dug under, jumped over, or broken into (using strong welded mesh). personally I argue foxes are more of a risk due to the fact that they're out looking for food and opportunity, most cats are looking to play vs eat, as they're fed in a house. so going to the bother of a rabbit in a pen probably isn't worth it. obviously some may try, due to instinct, but I feel a fox would be more determined due to hunger & instinct.
rabbits can die of shock/heart attack. however providing they have the safe space to retreat (lots of hides) I believe it minimises the risk - hopefully somebody can correct me if not. the "rabbit had a heart attack and died" is something very commonly spread around, but it also comes from a time where rabbits lived in tiny 3ft hutches. they had nowhere to hide too away from the predator. rabbit care isn't always what it is.
unfortunately moving rabbits in & wouldn't work either. rabbits can't handle a temperature change bigger than 10C - so once you hit autumn, winter & early spring, taking them in and out just won't be viable any more. not unless you can make the temperature inside the same as outside (no heating, all windows open). coming from the cold outside to hot inside will cause them to instantly shed their winter coats, and even cause stasis due to the stress put on their system of being so hot.
I also feel moving rabbits about like that might cause them stress. rabbits usually like to have their territory and stick to it. being in one territory overnight, and then the other during the day, may not sit so well. they might want to stay in the outside territory, or the indoor one, and be unhappy at being forced into one (or the other).
rabbits are very all or nothing characters - you can't have a bit of both. its either in or out, or once place or another place (or the choice to transfer freely between to spaces).