You should submit only one version of the paper. Think of the referee as a typical reader, not a judge providing a certificate of correctness. If the referee needs additional information, then other readers will need it too.

Regarding putting a proof in an appendix: There are exceptional cases when this is necessary, but most often it is not, and it can even be annoying to the reader (or seen as a warning sign of a bogus paper!) when important arguments are removed from their context.

Reading a math paper will always be time consuming, but I don't think there is a general convention that proofs should be sketchy. As an inexperienced writer, it is sometimes hard to know when something should be left out, and when leaving it out will be regarded as a gap. Feedback from teachers and supervisors on this matter can be contradictory and confusing. If you feel you still haven't got the knack for it, bear in mind that it is much easier for a referee to ask you to remove details than to figure out when they are missing. I would not endorse any general advice to write sketchy proofs in order to keep the paper short.