Precious as was the company of her daughter to her, she [Mrs. Dashwood] desired nothing so much as to give up its constant enjoyment to her valued friend; and to see Marianne settled at the Mansion-house was equally the wish of Edward and Elinor. They each felt his sorrows and their own obligations, and Marianne, by general consent, was to be the reward of all [Col Brandon’s sorrows]. (50)

I think Elinor did tell Mrs. Dashwood about both Elizas. I think she would wish her mother to know so that she would be in a position to help Marianne deal with the information. Also I think Col Brandon’s disastrous first attachment would only endear him to Mrs. Dashwood. Telling the story of the first Eliza explains why Col Brandon is the second Eliza’s guardian and also that she is not his natural daughter as rumor has it. I do not think Mrs. Dashwood is meant to understand Col Brandon, like Willoughby abandoned his lover and has an illegitimate child from the affair. We know Mrs. Jennings thinks nothing of the idea but to Mrs. Dashwood, with “a sense of honour so keen, a generosity so romantic” (1) it might not sit so well. I searched the text for something definitive but the best I could find is in Ch. 50 above. Mrs. Dashwood, Elinor and Edward each felt Col Brandon’s sorrows rather than sorrow which suggest the story of both Elizas was given to Mrs. Dashwood and eventually Edward. Does anyone think Elinor only told Mrs. Dashwood the Eliza story that concerned Willoughby? (:D)