Availability of TS in Mexico in June, is like shooting fish in a barrel. The reason is it is not the desirable time of year. Assuming you are set on a June date. I would never do Cancun, since it is basically reclaimed marshland and jungle, and that is a huge no no. Next, Western Mexico beach towns, are a better choice. I personally like the variety and the high quality of resorts in Cabo San Lucas.
I would advise you not to trade into a Hilton resort, but instead use 4800 HGVC thru Hilton/RCI and get a two bedroom at all the RCI resorts. Go on line and check out Pueblo Bonito Sunset Beach, your whole family will love it. Super clean, upscale, modern, and a destination resort that most people only leave the grounds on the free shuttle to the sister resort in the heart of the marina, which offers a pleasant excision for lunch or diner and windows shopping.
I would sooner suggest you use your 4800 Hilton RCI points and get on the wait list for a 2 bedroom Hilton, wherever you which to go and simply rent a June location in Mexico or elsewhere. Hilton points are to valuable to exchange into mexico in June, but that is my opinion and you can certainly easily get the exchange you want.