San Diego has a big market of school year or “9-month” rentals. The lease goes from Sept to May, and after that you vacate so the owner can do a weekly vacation rental.
So if those are the 9 months you want, you can get a pretty good deal. You can also get part of the summer at the higher weekly rate.
Otherwise, I suggest you just look into people with long term rentals and explain you may need to leave in 9 rather than 12 months and can pay a little extra for this flexibility.
Reasonable price detached house in a good district and near La Jolla? University City or North Clairemont would be my choice.
Depending on where you are coming from, they may seem expensive or cheap, but overall San Diego is more expensive than Delaware. If being very close to La Jolla isn’t needed, all areas along the entire 52 are nice and the highway ends in La Jolla so it remains easy to get to. Prices don’t really go down as you head east, but the houses are larger and newer.
When you budget, keep in mind your heating and AC costs in San Diego will be very low compared to the NE, and are especially low near the coast when winter lows are rarely below 50 and summer highs rarely above 80.
I think San Diego is one of the best places in the world to work from home, and the number of mid-career professionals and small company owners who do this is huge. I think north county probably has more than the city itself and the inner suburbs.
Final point about La Jolla and schools: the local schools there have declining enrollment due to population aging, so it is easy to get your kid into LJ elementary schools if you’re willing to do the drive. The kids will be very welcome because the schools risk closure if student population falls too much, which is what happened in Mission Beach.