Indoor cat, day 1

We're having a bit of a stressful day or two with our new cat, Dory. Well - not so much with her as with the neighbour cat. It's our own fault - we used to let him in and he'd lounge around the house. But that was before we got Dory. Now we're trying to decide how to keep him out. There's only two options, realistically. Either Dory wears a collar so we can put a magnetic / infra-red cat flap in, or she becomes a house cat and never goes out again. We know she likes to be outside, and we know she freaks out when we put a collar on, so it's a difficult decision. We covered the cat flap early last night and she didn't seem to make any motions to go out. I kept it covered this morning after feeding her and she stayed in, obviously. But when Paula went to do the litter box this morning, she found Dory had pooped on the carpet for the first time. I hope this was an accident - a bum too close to the edge of the box or something. I hope this was the case and not that Dory is protesting to being kept indoors at the moment.