A gift is yours once it is given to you.
From that perspective, the gift of stock is yours (family, not you individually) to do with as you please.
I, however, would want to honor the kindness and thoughtfulness of the gift-giver. Why did she give the gift in stock? Was it because that was what was available to her to give? In which case, I'd be fine with converting to to a more user-friendly medium for my family. Did she give it for a reason? In which case, I'd want to learn more about that reason before deciding. The gift would still be our family's to do with what we please, but I just would want to honor the thoughts behind the action.
As for how your family decides to use the gift, that depends on your values. If you are asking this question, I suspect there is a reason. Honor your feelings.
If grandma is still alive, is it likely she will also give a gift to the new baby? Perhaps grandma intended it to be a gift to be split amongst any/all of DH's children? Personally, I wouldn't worry about the unequal amounts of money given to each child AT THIS POINT in time. You have a lot of time to figure that out later.
For me, the ethical question cannot be answered until it is known what grandma's intentions were with the gifts of stock. That's just me.
As an example, various relatives have given individuals in our family gifts of cash at various points. DH was free to do as he pleased with his; I was free to do as I pleased with mine. It was an open discussion and dollar amount DID matter. I asked each gift-giver about the cash gifts for DD. One person wanted the CASH to be there for DD later on, so we opened a savings account for DD. Other folks just didn't know what to send, so DH & I decided each time what to do with the cash gift. The result was different each time. As her parents, we are responsible for caring for her and making these decisions. For us, it was okay to use cash gifts for DD for non-gift type things that would benefit her directly, such as swim lessons or cloth diapers. When we were both unemployed one Christmas (DD was 9 months old), cash gifts were okay to use for essentials for her (for us). As DD has grown (she's 10 now), we've given her more and more of a say in how she handles these things...preparing her for adulthood gently.
I cannot say for sure, simply because I haven't been in the position you are in, but I'm fairly confident I would not choose to sell a stock gift given to my DD and use it to pay my own student loan. The reason of better quality of life for the family doesn't work for me. However, I don't know the quality of life we're discussing. Is there a degree in hand and the potential to earn an income? If so, then I would keep the gift for DD (dealing with potential siblings later) and let quality of life sort itself out with the income potential from the degree earned with the student loan money. If no degree was earned and/or the potential income earnings was otherwise restricted for some reason, then I might act differently.