My thought - ask mom if it's okay to use the money to pay down the 2nd mortgage, abide by her wishes (pay off the student loan if that's what she wants).
Whatever you decide, you will be $20,000 better off
Math & calculation asides:
Is your 2nd mortgage payment interest only? If so your effective APR may be higher than 8.625%, or there could be some insurance/fees/something in your $227.51 payment - or my math could be off! My math: simple interest 8.625%/12*27,000 = $194.06.
Doesn't really matter, but means my quick-calculation will be off in the following because I assumed the $227.51 payment is all interest:
+If you pay your student loan off (assumes you have some money to combine with mom's) and add that $109.72 payment to the 2nd mortgage payment, your balloon in 8 years would shrink to somewhere in the $4,500 range instead of $27,000 (because you will have paid off principle along the way - balloon closer to $2,600 if rate is 8.625% and my math is right)
+If you use the $20,000 to pay down the 2nd mortgage and continue making payments of $227.51/month on it, you will have paid off the 2nd mortgage completely in about 3 years (about 1 month faster if rate is 8.625%)