When you say 35 feet, do you mean 35 feet from the apex of the triangle to the back wall of the conservatory, or 35 feet square, i.e. 6 ft by 6ft ?
You're saying it's big enough for people to have a barbeque, and for a trampoline, so I guess you mean 35 feet deep to the apex of the triangle.
Is the garden really so small, or is it just badly designed?
Often, bad garden design emphasises the edges and walls of a garden, which makes the garden look much smaller than it is. This is especially the case with small gardens - people put the emphasis on growing things up the walls, which means that you look at the wall, not at the space between the walls.
You can really have an astonishing impact on the feeling of the space by re-designing the garden layout.
I'd go for the house, and get a professional garden designer to design the garden. If you can't afford a professional garden designer, ask on here! Off-hand (and depending on kids ages), I think that the thing to do would be to put the trampoline right at the tip of the triangle, and to have large plants in front of this forming a green wall (perhaps bamboos), so that from the house, you can see there is more garden, but you can't see how far it goes or what it is. You can even put a garden mirror on the far fence opposite to the gap in the 'wall', so that from the main house the garden appears to go on and on. Then you put a lot of tall, colourful flowers in a border in front of the green wall, so that the eye is drawn to those, and then have your terrace going from the house to the flower border.