Hi and welcome to CT. If they let you rub and "love on them" and you are careful about their head swinging which can hurt you without their meaning to... I see no real reason for a chute. Get a halter on them and let them drag the long end... if they step on it they will learn to stop and they will not hurt themselves with it. You don't have to leave it on them day in and day out... just enough for them to get the idea of it is not going to hurt them. once they get to where they pretty much take it for granted. then tie them to a very stout pole or tree, and they will learn they can't get away from it... they might fight it but it should not take them long to learn that "it's no big deal".... and that gets them to learn that they just can't pull and get "away".... from there, leading will be simply using a small bucket of grain to tempt them to walk forward to it as you are "leading them".... and soon they will go most anywhere for you because you give them a "reward" for doing it. If they were calves it would be a little different, but you are dealing with older, bigger animals... They have to somewhat think that "they are doing it" ... not that you are "making them do it"....
Does the vet think the "heiferette" needs feet work? Alot of cows get cracks occasionally... just keep an eye on them... it could be from extremely dry ground, and her being overweight...
"PET" cattle are hard to move... as
@Brute 23 said... they will often follow but you cannot drive them anywhere. They can be a pain in the butt... BUT.... cattle trained to come to call, for a little handful of grain as a treat... or... a person I know gives them just some plain white bread and they like to take and eat a slice from your hand (fattening, but as an occasional treat it works). We have cattle that will load right out in the field into the trailer if we put some grain in there and then open the doors for them... I suspect your animals will get to that point... you should be able to entice them into where you want them with the promise of a little grain...
It is probably good the older one can't breed at this point. Her pelvis is unable to "stretch" to accommodate calving and it could wind up costing you for a cesarean, or problems that could kill her... The younger one is a good candidate for breeding AI... and a simple "chute" with a couple of gates that you can put them in... and that will not swing open... would be sufficient.... BUT..... when they come in heat, sometimes they are "moody"... and might not do what you want , or what they would do the rest of the time... The "medina hinge" type chute....would work for something like that ... if you do some studying on it, and have a place that you can use that will be sturdy....something as simple as that for what little work you may need to do with them.
If they were to get hurt for any reason and you had to have the vet out, a simple way like that to contain them and if nothing else, he/she can give them a tranq if they need to work on an injury or something.
I would not invest in a trailer at this point. Find a neighbor that could haul them to the vet or something if needed... as stated... if you use it twice a year, the tires will dry rot off it . Some vets have portable chutes, on wheels, they will take to a farm around here in Va.... or have a fully functional system at their office and you can haul your animal there...
@Jeanne - Simme Valley shows her registered cattle and would have better tips for halter breaking but most of hers are halter broke alot "smaller" than 1500 lbs... :rolleyes::ROFLMAO: