All perfect praise be to Allah, The Lord of the Worlds, and peace and blessing be upon the Messenger of Allah, his family, and all his companions.
There is nothing wrong with a woman wearing tight clothes for her husband, whether they are sports clothes or something else, and there is no ‘Awrah for the spouses towards each other, so it is permissible for each of them to look at any part of the other’s body, as mentioned in a hadith in the Musnad of Ahmed and others that the Prophet, sallallahu ‘alayhi wa sallam, said: "Protect your 'Awrah except from your wife or what your right hand possesses." It is also permissible for them to set up a beach-like environment in the way described, and sunbathe wearing a bathing suit if they are safe from being seen by any foreigner.
This act does not fall under the imitating of disbelievers that the Sharee’ah disapproved of, for the disapproval here is related to imitating them in what is specific to them, and not in what is common. Such custom and tradition matters are not forbidden except what specifically pertain to the non-Muslims, so it is not forbidden just because they do it.
Recreation in permissible matters is a good thing, and it helps in carrying out the obedience acts. It was reported that the following quote was of the wisdom of Al Dawood, peace be upon him: "The sane person should have four hours: one hour in which he prays to his Lord, one hour in which he holds himself accountable for his deeds, one hour in which he is alone with his companions who honestly advise him and tell him about his faults, and one hour in which he enjoys himself with what is permissible and beautiful, for this hour will help him in the other hours.
Allah knows best.