If you aren't worried about schools then Ayrshire or Inverclyde coast ticks all your boxes and you would get a lot for your budget. Anywhere on the railway line from Troon/Ayr all the way up and round the Clyde coast to Greenock. Most places will be under an hour on train to central Glasgow, less to drive if ILs in suburbs.
Lots of sea swimming groups just search the town names on Facebook. Yes it's wetter overall, although there are still plenty lovely days and it's gorgeous even in the rain with views across the islands from every town and village. I am from the east coast now live on west coast and I genuinely don't find it any worse. Or the midgies. Puzzles me why it's always mentioned on here. Really only an issue at dusk and smidge repellent works well. It's certainly not enough of an issue to factor in such an important decision.
Gourock is a pretty town adjacent to Greenock with lots of facilities. Stunning views from many properties.
Largs is very popular with retirees and is a bit more touristy (and middle class) with associated facilities. There are also quite a lot of English residents so you wouldn't be so out of place as you might find in some of the other towns. Ardrossan (part of the "three towns" has some stunning traditional seafront properties that come up at amazing prices) and does have local facilities but it's quite a different demographic from the others I mention and I suspect you might find it harder to blend in not being a local. Prestwick is meant to be quite nice but I don't know it well. Irvine/Troon/Ayr are all bigger towns.
Some of the villages (wemyss bay/skelmorlie/Fairlie) are lovely but don't meet your criteria on facilities which is also why we ruled them out. Seamill attached to West Kilbride is gorgeous and has some facilities and lots of crafty shops in the village so might be worth a look but we still found it too small.
Although I don't know it so well the recommendations of Helensburgh and that coast are worth a look. Particularly if your in-laws are to the north of Glasgow.
Even as a born and bred east coaster I don't think that's a good suggestion in your case. Just signing yourself up to a lot of long boring stop-start drives along the m8. Which is even more grim from October to April - don't underestimate just how long and dark Scottish winters are. On the flip side this time of year is wonderful.