As a 2nd year undergraduate, what should I do to enhance my maths grad school application if I don't get into noteworthy summer programs?
If you have one bad semester, particularly just a couple of bad grades in non-major courses, it's not going to torpedo your PhD application, though to show it's not a concern, you should do very well in your major courses, taking what advanced courses you can.

For the summer, programs such as REUs can help broaden your perspectives.  These are also nice because they give you money and a chance to work with other interesting students.  However, another common option is to find a professor, say at your university, willing to work with you over the summer on a reading course or a research project (possibly informally).  Several of our faculty do this semi-regularly (I usually travel in the summer, though I've done it a couple of times), sometimes with a group of students, so try asking around in your department.

I personally think reading courses are just as good, if not better than, most undergrad research projects because at your stage the most important thing is to learn a lot of math.  While you can just read things on your own, a professor's guidance can be quite valuable.  Also it will provide an opportunity for you to get a more meaningful letter of recommendation, which is very helpful in applications.