Tips for how to change a line dress into mermaid?

See if you can find a dress pattern in the shape you want (mermaid) in the correct size. Take out the skirt pieces from the pattern and lay them on the A-line skirt of the actual gown. If there is enough fabric, then you can convert it to a mermaid gown. Make sure that the top of the new skirt will fit onto the bodice of the old gown. I hope it works out for you!

Find a pattern that suits you. Then very carefully disassemble your mom's gown and reconstruct using the new pattern. It is going to take some fiddling, adjusting and even hair pulling, but it can be done.

Or take to a custom dressmaker to do for you, but expect to pay dearly for it. Working with wedding fabrics is a bit trickier than making a regular dress.

Unless you have experience with this sort of fabric, take it to a seamstress. A few weeks ago I was getting food from a place that was next door to a cleaners. There was a girl in the cleaners wearing a wedding dress. I remarked how pretty she was. She told me that she was "transforming" a family wedding gown. Moral of the story: check the prices at your local cleaners. I think you might be surprised. Best wishes and congratulations to you.