You can set specific day amounts between moves, new relationship after break up, etc. I'm sorry I can't remember where exactly it is located but I assume it was on the setting for "All sims".
When I first started my game (and many townies were still looking for a spouse), it felt like the townies were changing partners and moving very often. So I changed those day amounts higher. I didn't change the speed. The pace seems to have cooled down a lot.
There are still some sims who simply can't seem to stay in a relationship (Jared Frio and VJ Alvi) - I guess it's because they just are rude. It's fun, actually.("Personalities" of the progression affect, I assume)
About the moving thing - Most EA built houses don't really have enough cribs, single beds etc. Especially in SV, some large family homes have no cribs and only 1 bed for a child! So I recommend adding beds because StoryProgression checks the bed amount and moves the family out when they get more children, if there are not enough beds.