Short answer: I obviously can't predict the future but do not see snap elections on the horizon short term.
Longer answer: It's mainly the FDP that keeps stirring up trouble within the coalition but their poll numbers are just as abysmal as those of their partners, if not more so. They would likely loose votes in a snap election so have limited motivation to drop out. Maybe if they had reason to believe that they would at least get the neccessary 5% AND a coalition with the CDU (but the CDU is also flirting with the Greens).
These regional elections will be hard for all three coalition partners, sure. However, they have always had a hard time in the East. That is nothing new. What's new is two populist parties polling very strongly in the East and dwarfing even the CDU. In all this talk though (as in the eternal debates about how supposedly nobody ever talks about the East and how the East is so underrepresented, etc.) it is often left out that the East only makes up 1/5 of the country, populationwise. Germany is not divided in two equal parts, it's one big Western chunk and one small Eastern appendage. That appendage, which is also more rural, economically weaker and has an even older and whiter population than the rest of the country and is losing its young talents in a braindrain, has its own political culture and lots of accumulated anger and bitterness. So if the federal government ends up drastically losing support in the East that will definitely not improve the national mood. It will not make the country ungovernable though.
All of the 16 Länder represented in the Bundesrat have coalition governments. 12 have the SPD in their government, 10 the Greens, 9 the CDU, 3 the Left and 2 the FDP (plus the Free Voters in Bavaria). If the AfD enters into the government of all three states that have elections next weekend (unlikely) and could rule alone or totally dictate their terms there (even less likely) that would give them 12 out of 69 votes in the Bundesrat. Not enough to do or block anything.
The AfD is currently polling at between 16 and 19% nationally. That is a lot and a good reason to worry indeed, but far from the 30% or more that they have in some remote rural areas in the East. And even in those areas where they have huge support the vast majority opposes them. The thing is that an SPD supporter might not like a CDU governent but it will tolerate it and vice versa. But the AfD is not just any other party and the country, rather than being split into seven social groups for seven parties, is basically split into AfD and anti-AfD. Most non-AfD supporters hate the AfD more than they hate each other which is why suddenly even coalitions between the center right and far left are considered an option.