Welcome to ECF, paws_fur_me!
There are two aspects to your question:
- What model of e-cig (i.e., the hardware) looks and performs most like a 100s cigarette?
- What flavor e-liquid or cartomizer (that go into the e-cig) tastes most like Doral Light?
Hardware
nerf's recommendation of the Joye510 model is an excellent answer to the first. It is the most popular and perhaps best performing e-cigarette today. Some of the most inexpensive and respected suppliers of it are
Cignot,
Rocky Mountain Vapor, and
NHaler.
There is another model you also may want to consider: the
Kr8. As a two-piece unit – battery and cartomizer (integrated atomizer and cartridge) – it is the simplest and easiest to use. Filling with e-liquid is not required (although it is possible and, over time, she probably will choose to refill the cartomizers with juice). You simply charge your battery, screw on a pre-filled cartomizer (in any of scores of flavors and several nicotine levels) and vape.
It is sold by myriad suppliers and under several brand names, including:
NHaler (KR808D-1),
Vapor4Life (Vapor King),
PureSmoker (Ace),
CigEasy (Easy),
GoodProphets (VapoRite),
LeCig (D1), and
VaporKings (KR808D-1). Those are just the ones I've dealt with.
My suggestion is that you hold off getting enhancements to the basic e-cigarette, such as a USB passthrough, PCC (personal charging case), or battery "mods" like the Chuck or Silver Bullet. I think these would be overwhelming for a first-time vaper. Once she settles in on a model she enjoys, any of these can be purchased based on her needs.
Cartomizers (for the Kr8)
555-flavored cartomizers are sold by
NHaler,
Vapor4Life,
CigEasy,
LeCig, and
VaporKings. I don't know of any cartomizers prefilled with Mild Seven.
E-liquid (for the 510, or Kr8)
Cignot carries
Mild Seven (only 5 ml bottles VG). If 26mg is too strong for her*, combine it with their
0mg Mild Seven. And they also carry VG
555 in 20 ml or 5 ml bottles, 0mg and
26mg ... and PG
555 at 26mg only in both sizes. A great many suppliers carry 555; Mild Seven is a bit tougher to find, although
myFreedomSmokes also carries it (as well as 555 and many others) at various nicotine levels and bottle sizes.
* If she is/was a Doral
Light smoker, 26mg probably
would be too strong for her. A 50%/50% mix of 26mg and 0mg yields 13mg, which may be in the right ballpark. The percentages, of course, can be adjusted, but require higher level math.

While you're at Cignot or mFreedomSmokes consider getting 5 ml or 6 ml bottles of
other tobacco (or even non-tobacco) flavors. [For example, if my distant memory is correct,
Parliament and
Kent are mild-tasting cigarettes like Doral. myFreedomSmokes carries both; Cignot carries Kent.]
You (and she) never know what she might like in e-liquid. My favorite tobacco flavor thus far is DK-TAB, which doesn't taste
anything like the Basic UltraLights I used to smoke.
I hope you and your Grandma
enjoy your exploration of this exciting world of vaping!