Good grief. I can sort of see why the daughter (and the new boyfriend) might want to reach out to you, but it's way, way too much and way, way too soon. I don't see anything necessarily sinister in either text, even the boyfriend's - he may be picking up on some of your mother's anxieties and trying to mend fences on her behalf, but it honestly isn't his place.
OP, I'm sure you've checked this already, but I really hope they haven't sent similar texts to your brother and sister. I can see that getting terribly painful for all concerned. I agree with the PPs - do talk to your mother about this and ask her to tell boyfriend and daughter not to contact you again. The response will show you whether you need to start worrying.
(Regarding the 'way too soon' comment above, my mother died in 2009 and Dad remarried last year. Very fortunately, he has married a lovely woman with whom I'm becoming good friends. But even so, when he first let me know he was dating her it was a Big Deal for me. And I'm 39!)