Definitely sounds like you need two detectors for the indicated applications, as you really require a PI detector for gold, and preferably a VLF for coinage. For parks and dabbling in some gold/relic detecting, you have a lot to chose from, including the Minelab X-terra 705 Gold pack, Whites MXT All Pro, Fisher Gold Bug Pro/Teknetics G2, and the Garrett AT Gold/AT Pro.
You could buy a more dedicated detector for parks, but I only suggested the above units due to the flexibility of them being usable in both areas, plus the kids or your partner can also use it whilst you are out looking for gold. Despite being mainly gold detectors (bar the AT Pro), they are all very capable coin/relic detectors. They range in price from $850 (705) through to $1245 (MXT All Pro).
I am not going to recommend any single detector out of that lot, as I don't have specific experience on all of them, they are mainly listed due to being similarly specced, and to give you an idea of what is around (some of the frequencies/features also vary).
The remainder could be spent on the Whites TDI Pro Oz or Whites SPP for more dedicated gold detecting, with the left over cash used for a pinpointer/s, decent headphones, picks, plastic scoops, and some extra coils. As Wal & Liz have shown, the TDI is indeed quite capable in the goldfields. The TDI Pro can also be set up for and used successfully for coin shooting, as proven by some forum members (albeit with some compromises on lower face value decimal coinage). The TDI Pro Oz sells for $2295, and the SPP for $1195.
As mentioned above, the popular option for serious gold detecting is the SDC2300, it clearly has the runs on the board as proof to its effectiveness, but just have to keep in mind that you won't have much change from $4000 for anything else, nor have anything suitable for coin shooting etc.
You could just bite the bullet and get the SDC initially, then pick up a VLF for coins down the track if the budget is stretched too far.
Decisions, decisions!