Let's see lady's steps to know what's the difference from her point of view (always do this, because you want to 'manipulate' her by your leading!): At a heel turn Lady has to CLOSE FEET on 2, so after 1 she doesn't swing to the side but pulls her LF towards RF.
Because of this you have take care not to transfer your side swing between 1 and 2 to the lady, by taking weight a little longer over your LF e/o 1, so that she feels that she has to turn on one spot (the point where her RF arrived e/o 1). This may be felt as "releasing hold a little bit" BUT this effect of course must not be seen from outside the couple, because otherwise the dancing hold looks wobbly!