How do I fix a condensate drain line that froze in my split electric system with heat pump?
Your inside coil should have two outlets to drain condensate, one running outside and the other with a float switch to shut down the unit if the outside drains clogs. You can unscrew that float unit and put a bucket there to drain the condensate until the line thaws.

You should also figure out how to correct your condensate line so that it can not freeze. In climates where freezing of the condensate line is possible, you have to run it so that you maintain an air lock on the line (with a p-trap), but also do not expose the water creating the air lock to freezing temperatures. like this:



Notice that, starting at the a/c unit, the condensate line has in this order:


an air gap, which is basically just a t-joint with a short piece of vertical pipe, left uncapped and open to the airspace shared by the air handler or the conditioned space. It should be a couple inches taller than the condensate collection pan, otherwise the condensate will flow out of this tube and never trigger your shutdown float switch, if you have one. The air gap prevents the p-trap from being sucked or blown dry by the air handler.
a p-trap to prevent your conditioned air from being blown out the condensate line, or from sucking in fumes from outside. It also keeps critters out.
a continuous down-sloped condensate line.


All of this needs to be laid out so that everything from the air handler through where the condensate line starts its downward slope will not freeze. Since the line is sloped down, it will drain, even in cold weather. It's also important to minimize the amount of line exposed to freezing weather in order to prevent the water from freezing in cold section of the line.

Also, in emergency heat mode, you may not be able to generate enough heat to keep the house comfortable. It used to be that the emergency heat coils had to be large enough to heat the house by themselves. Since heat pumps have been on the market for quite a while and their reliability and availability has improved, that is no longer the case.