No you can't tell the mom the day of! You have to discuss this before the plans are set. What CoCoMom said is right - the mom goes and shops and prepares, and THEN finds out there's an issue and you have a list of requirements, including instructing her on the use of an epi-pen? That's not going to work. In fact, it's going to tell her that you are not considerate and that you expect her to adjust at the last minute.
You are putting all of the trust in your daughter to use her epi-pen in the throes of a reaction. That's a lot to expect. 6 year olds forget where they put their shoes and their backpacks. When I was teaching, all of the teachers and other staff were instructed by the nurse in the use of the epi-pen, and we practiced with a dummy pen made for this purpose (no needle but we still had to press it into the thigh, and we had to practice sitting the affected child on our lap, assuming the child would not be able to manage this, either because of the reaction or the panic). We did this every year because, frankly, people forget how to use epi-pens if a long time passes between initial training and actual use. (The same goes for refresher CPR courses.) I can't imagine any parent who is remotely familiar with this situation to be comfortable putting a guest child in charge of her own allergies. That parent is also not going to want or allow that epi-pen anywhere where her own child can get at it, and that includes being in your daughter's possession. 6 year olds cannot be in charge of regulating the behavior of other 6 year olds.
All of my friends whose children have allergies have hosted the first play date at their own homes, and they let the other parent know up front. That opens the door to finding out of the other family's child has a similar issue, and lets them know whether to send a snack or not depending on what everyone can eat. A good friend of mine whose child had pronounced but not life-threatening reactions to egg and soy would tell the other host parent that the child couldn't have those things. But the same child also had an anaphylactic reaction to peanuts, so much so that they put a sink in their front hall and all guests had to wash hands upon entering. So there were very strong requirements if she visited another home, and my friends just never left her alone. They've since gotten rid of her soy and egg allergies entirely so she can eat those foods, and they've reduced her peanut allergy to the point that she can go to places that serve them as long as she doesn't eat them herself, so the parents only have to tell the host parents that there's a peanut allergy, and if they hear any confusion they just say they'll send a snack along with their child.