I really don't think this is a problem.
If there's a good / logical reason to combine the papers (and such a thing is possible by timing), that's fine. But there might be many reasons why it's not appropriate - in addition to what you mentioned above, there might be two different sets of coauthors on the different papers, which can also make it tricky...
However, if paper #2 has already been submitted/accepted/published/is not easily combine-able, then I think you should resubmit #1 at your convenience, to whatever journal is most appropriate. I wouldn't worry about paper #2 really at all in this decision.
In many subfields of mathematics, dissemination of results now happens largely on the arXiv. Thus I think where / when the articles get published is becoming less and less important (although the prestige of an article in a good or top journal can still be useful for career reasons).
I've certainly been in situations like this and it hasn't seemed to be a problem. I've also been a referee of papers in this position (both #1 and #2). In the reports for papers #2, I usually note something like: "this paper builds on the work of paper #1 which appeared 3 years ago on the arXiv...."
Best Answer
One I have heard of is the Italian school of algebraic geometry, 1885 to 1935.