Usually there's a separate party room for the food to be set up in, is that how it works at your place? You put the cake and anything else you're bringing in there.
Some places will reserve an area of seating for party guests. Check if this applies to you and if so know where it is.
Wait at the entrance with your list of people, say hi when they arrive, show them the reserved area if there is one. Collect up presents and put them in the party room.
Kids play, parents sit around and chat, buy their own teas and coffees.
Soft play place will announce that play time is over and everyone should go into the party room for food and snacks.
10 minutes before then end you clap your hands together and say "time to sing happy birthday now", sing, blow out candles.
That's the universal sign for parents to start collecting up their kids. You cut up the cake, give each kid a party bag and a slice of cake.
Guests leave, you collect up all the parcels, go home and have a stiff drink.
Good luck. I also hate hosting kids parties.