I have had so many emails from players about this that I finally in desperation decided it merited a post of its own.
There are two ways to unlock the first Hot Springs in the original HM DS. The default method is by having a child. Most players prefer to unlock the option earlier, however, by experiencing Flora's 3rd Heart Event in HM DS and her 250FP event in HM Cute DS.
This event is one and the same in both games. Here is the schedule:
3rd Heart Event, aka Blue Heart Event: walking from Vesta's farm to Waterfall on any sunny day except Sunday, 11.20 p.m. to 12.00 a.m.
Note that you must enter the screen walking from the windmill area north towards the tent.
The prerequisite in the original HM DS actually has more requirements simply because you must experience all heart events in order and therefore must have experienced the first two before you can experience the third. In Cute, the only requirement is that Flora must be at 250FP.
Please pay careful attention to the time given in the schedule. A player once told me he could not experience Flora's Blue Heart Event even though he had been to the right location at 11.20 in the MORNING every day... The event occurs late at night, not in the morning. Go there between 11.20 p.m. and MIDNIGHT!
I had thought that one could unlock the first Hot Springs by having a baby both in the original HM DS and in Cute DS, but I personally never waited that long in either game. I always try to trigger all events as early as possible. It is possible that, because Flora's Event in Cute is based on FP rather than AP and therefore can be experienced both before and after your marriage, that it is the only means by which the 1st Hot Springs can be unlocked.
If I ever have a chance to play a new game of Cute again, I shall have to avoid raising Flora's FP to 250, have a baby and see if the first Hot Springs are unlocked by any other Event as in the original HM DS. Meanwhile, if any player would like to confirm to me that the 1st Hot Springs are NOT unlocked by an Event (apart from Flora's 250FP Event) at any point after having a baby in Cute, I will add the information to my Guide.