If you live in TX, keep them separate because TX does things differently.
Anywhere else though, look at the rate and payment of your current mortgage, figure out the payment of the new mortgage including the $35k cash out, and then consider the existing mortgage payment and the new home equity payment. Write it all out on paper and you'll be able to see which is most advantageous to you. If the lowest payment is your primary concern, look mostly at the dollar amounts, but if the overall interest is a bigger concern, multiply all the payments by the terms and compare the final numbers.
Have you also considered student loans and work study? There are also grants to be had but it takes a little digging to find all the resources you might need. I managed to go to college with only one $4000 loan for the first year. After that, Pell grants and the grants from the school paid the tuition and I had a work study job to keep me afloat.