I couldn't find similar question being asked here. The closest one I can find is When to split/merge papers?. Here is my situation: I proved a theorem. When I try to type it, I found that it's very long. Since it's long, I splitted it into two parts. I finished the first part (50+ pages) and submitted to a journal few months ago. Now I almost finished typing the second part which is also 50+ pages. My question is: Should I submit the second part to the same journal? If I submit to the same journal, probably the editor will send the second part to the same referee. Then the referee who is familar with the first part can read the second part more easily. However, as we all know, it's hard to publish long paper, I think it would be even harder to publish two long papers in the same journal. However, if I submit to another journal, it may be even harder since the new referee may find it difficult to read the second part without reading the first part. So this also gives me the second question: should I wait until the first part is published/accepted, and then submit the second part?
Since the two papers together prove one main theorem (if I correctly understand the first few lines of the question), it seems reasonable to submit them to the same journal. I can imagine a referee or editor being unhappy about being asked to publish part 1, which builds up to a big theorem that will appear in a different journal.
It's true that it can be hard to find room in a journal for very long papers, but I assume the journal doesn't mind publishing papers of 50+ pages at least occasionally (otherwise you wouldn't have sent part 1 there), and the difficulty of finding space is no worse for two of your papers than for one of yours and one of someone else's. The main effect of space shortage in such situations is that the two parts of your paper might appear in different issues of the journal.
I've published multi-part papers with all parts in the same journal. The splitting into parts was forced by the journal's upper bound on the length of papers, but I don't recall any complaints from the editors about my submitting several parts, each close to the upper bound. In at least one such case, the parts ended up appearing consecutively in the same issue of the journal. (The only time I've submitted "parts" to different journals was when they were really separate papers, though on the same topic. Two parts were really logic and appeared in the Notre Dame Journal of Formal Logic, and one part was, at least in my opinion, of broader interest and appeared in the AMS Transactions.)
One option to consider, which we did with the small index subfactor papers, is to submit to the same editor but at different journals. This retains the logistical advantage of having the same referees, but doesn't require as much space in one journal. Furthermore you can put the better half in a better journal.
I usually do not split in such cases, but if you do, I guess the same journal is a better choice, especially if you think of the poor people who will have to look up and reference your paper in the future :). Also, if possible at all, I would include into the first part a forward reference to the second one (if the submission is to the same journal and the second acceptance occurs before you get the galley proofs of the first part, that may be completely feasible from the technical point of view). What I really do not understand in this story is how the referee is supposed to do his job being presented with the first part alone. I can imagine myself in his shoes writing something like "The paper has many interesting ideas and no flaws so far but it is completely unclear how the ends will finally meet..."
It is probably too much to ask from one editor to find space for two 50 page papers on the same topic, so it is natural to send the second part elsewhere. The exceptions I know involve solutions to big problems and/or big names.
About your second problem... include paper one as a helpful reference for the referee.
First of all, I wonder how you can be sure that a 100-pages-proof is correct before you even have typed it in completely -- at least unless it consists mostly of routine computations!
As to your question, I think one proof should ideally be given in one paper, or a least in two papers in the same journal. -- Well, of course there are some proofs distributed over MANY papers, like the one of the Classification of Finite Simple Groups, but that's probably something different ... .