What is the problem for an engaged couple to touch each other if the woman has been to the מקוה and is therefore pure?
Mazal Tov on your engagement, you should both merit to have shalom bayit and a bayit ne’eman b’yisrael!
Regarding your question, let’s first discuss the worst type of touching, having relations, (and unfortunately this is most probably what will happen).
. The Talmud (Kiddushin 81a) says that after the tragic story of Amnon and Tamar, King David and the high court prohibited yichud for a boy and girl to be secluded, even after the girl has been to the mikva. This is also brought in Shulchan Aruch Even Haezer 22-2. The fact that they are engaged to be married does not change this at all, in fact it make the rules of yichud more stringent, since the two are friendly with each other, and they are more apt to sin together.
Aside from this, even if she was already to the mikvah, it is absolutely forbidden for them to have relations, according to the Rambam it is a biblical prohibition, (Hilchos Ishus 1-4, Sefer Hamitzvos Lavin 355, Issurei Biah 18-1) and according to other rishonim it is rabbinically (see Chekas Mechokek Even Haezer 27-1) simply because it can’t be less than the yichud which in itself is prohibited. Therefore regardless of the severity of the prohibition everyone agrees that it is forbidden.
In fact the Rishonim (Rivash 425) say that it is for this very reason that single girls may not go to the mikvah in the first place, even though it is bringing the severity of the sin from a kares to only a lav, nevertheless, by her going to the mikvah she is enticing herself and other to think that it isn’t a sin and therefore she is causing herself and other to sin! It is for this reason that in general the mikvaot do not allow single girls to tovel, in order to prevent them from sinning, causing others to sin and thinking that it is really permitted. It is true, it isn’t as bad as if she would be a nida, but it is the same as saying that if it isn’t LSD and it is only marihuana it is healthy, permitted and fine
There is another point here, where many people make a mistake, and I understand where it is coming from, that when a boy and girl are engaged they assume that since they will IY”H be married, that it is as if they already are. In truth, halachically they are exactly the same as before they got engaged, and in a very a large way they have to act with each other in such a manner. They have to keep in mind that this girl/boy is a man/woman that is NOT (yet) his/her spouse, and halachically they are like any other girl/boy and proper distance has to be maintained. It shouldn’t be that hard, because it is only a matter of time until they will be married.
A side form this, by engaging in such activity, they are hurting their marriage, in a number of ways. First of all, one of the things we daven for is that the divine presence should rest between the two, as the Talmud says (Sotah 17) “if the two merit, the shechina rest among them, but if not then fire (anger and fights) consume them. How can one ask for this divine assistance if they are committing zenus together and driving the divine presence away from them? Besides, by “jumping the gun” now they are really hurting the specialness of their union when they will get married, because it will no longer be special, which can have a negative effect on their shalom bayit.
It is true that unfortunately there are engaged couple that make this mistake, but their impatience is really hurting them in numerous ways, and should not be done.
Best wishes upon your marriage