Definately do the difficult one first and if you can pick him up then just push him in quick. and slam the door.
I have a bad problem with Sasa cos cant touch her and the annual vet trip about 3 weeks ago is stressful for all. I had to shut all doors except the study where she was kipping on sofa and because she will run away from me if I get too close, walk up to her. She then rushed of sofa into the hall and I shut study door behind her.
Next stage was getting her to one end of hall and trapped with only place to rush into being the big wire cage, which was covered at one end with a towel.
She wouldnt go in and because the cage is big and I have no balance, it was hard to reach her cos she had glued herself to the door at the end. She is very heavy and if I try to lean over I fall, so was trying to use something to poke her out with to make her move into the cage. One never has all the things that are needed at a time like this cos cats are so sneakie!
It took about 30 mins of talking pushing and yes stroking cos she was trapped, before she rushed into the cage. It was so pityful cos she was squeaking and crying cos she was so scared and cryed all the way to the vets but was quiet all the way back (50 mile round trip) . As I pulled up outside the house she started banging against the door of the cage cos she knew she was home!
Cos she is so heavy it was hard to carry the cage to the door with her jumping around but once inside and cage open she was gone, outside, and I thought that would be the last I saw of her for 24 hrs at least but noooooooo
she was back in the kitchen under the table in the evening. Took her a week or so before she would use her sofa again though!
I know this sounds like a comedy but its so hard and hope that you are able to get to the vets less stressed than me