My two bits on your problem
First off, I am not a designer, but I do make fonts for projects. These are my thoughts and how I would do it. I also have an older Mac and can't upgrade until I can afford new licenses for the software I use. I have TypeTool as well as a few other Font making/modifying tools.
Generally, if one has the ability to modify a font, one can create one from scratch. They could have changed the name and other meta data on an already existing font that had symbols, or they could have taken <i>Equity</i> (by Matthew Butterick, foundry- MB Type ?) and replaced symbols in it. Perhaps the designer made the font and called it "Equity". I don't know.
Why they would modify an existing font that costs $120 for a license is a little weird, but I digress.
If you have already created the symbols in Illustrator, Vector Designer, or another vector graphics program, great. All one would need to do is to export each graphic as an EPS file and import that file into a fontography program and replace an existing glyph.
If not, I find it easier to create a symbol in a vector program first rather than create it with in a font making program, like FontLab or Typetool. I find the interface on those programs more difficult to use than in another vector graphic program.
I don't know what symbols you need, but I got a great book from Pepin Press called <i>Signs & Symbols</i>, ISBN 9057680556 (
http://pepinpress.com/catalogue/view/82 ) . It comes with a DVD with JPGS that can either be converted to an EPS, or better, used as a basis to create you own symbols. It's out of print, but this is the age of the Internet.
I'd have to see the font you are using, to see how it was modified or created. There is a lot data in a font, beyond it's name. I don't know how your designer made or modified the font, did hinting and kerning or to see what kind of font it is (TTF or OTF).
If you are concerned with the kerning, you can do your own ligatures sample and work it out from there, or perhaps he made it monospaced so it really doesn't matter.
Quite frankly, if you are going to spend money on a font design program, and you are only going to be adding symbols, you might just want to hire the designer to modify the existing font. It may cost less and it does give work to a designer, who's work you are currently using.
Another option is to find a font that has the *symbols that you need and use a program like PopChar (
http://www.ergonis.com/products/popcharx/ ) or a text replacement application to insert the symbol you need. I like PopChar for special symbols. A program like TextExpander can automatically insert a symbol when a string of text is typed. For instance, when I type "~scruple" TextExpander inserts the "℈" symbol for scruple.
It might just be easier and less expensive to change how you are working so you aren't using a font to insert symbols.
*- if you find a font that has the symbols that you need and it isn't a free font, get a license if it's for commercial use. A well made font takes a lot of work.