Check with her if she a gold or white gold/silver person. For years (until I went grey and my skin toned changed) I could not wear silver/white gold/platinum - truly made me look awful, awful awful - like a corpse - was most odd.
On the other hand a very dear friend of mine has olive-toned skin - she cannot wear yellow gold as (in her words) it makes her look like a parody of a pirate - the yellow/olive tones look like she should be Johnny Depp!
What a lovely thought. You could look at something which perhaps incorporates the child's birthstone (perhaps alongside the mother's?).
I have a pendant with interlocking rings with the names of myself, my husband and my two children which I absolutely love and wear all the time - was a present from my husband - I think from notonthehighstreet.
With that budget I would definitely be speaking to a local jeweller about making something bespoke. If you're near Birmingham you could check out the Jewellery Quarter as there are some amazing jewellery designers there.