She saw the tuhr then she had some discharge – what should she do?
We do not know what you mean by “a little bit of white discharge was coming out.” If what you mean is that you saw the white discharge which is the sign of purity (tuhr), then whatever yellowish or reddish discharge comes out after that is not regarded as menses, because Umm ‘Atiyyah (may Allaah be pleased with her) said: “We did not regard the brownish or yellowish discharge after the tuhr as being anything that mattered.” Narrated by Abu Dawood, 307; classed as saheeh by al-Albaani in Saheeh Abi Dawood.
Based on this, your prayer is valid, and there is nothing wrong with your having had intercourse, because you were not menstruating.
But if what you mean is that you saw that the discharge was still yellowish or reddish, this means that the menses had not yet ended. A woman should not be hasty in deciding that the period has ended when she sees yellowish or reddish discharge, no matter how little it is. The women used to send pieces of cloth to ‘Aa’ishah with yellowish discharge on them, and she would say, “Do not be hasty until you see the white discharge.” Narrated by Maalik, 130.
Pieces of cloth refers to what women use to check whether there is any trace of menses left or not.
See also question no. 66062.
Based on this, then you have to make up that day, because it is not correct to fast when one is menstruating.
With regard to intercourse, there is no sin on you in sha Allaah, because you thought that your period had ended, and you did not deliberately commit a haraam action. Allaah says (interpretation of the meaning):
“And there is no sin on you concerning that in which you made a mistake, except in regard to what your hearts deliberately intend”