If you don’t want an awful London commute, you really don’t want to move further into Bournemouth and Poole, you want to be Ringwood as the further over, max, so you can get the fast train from Southampton Parkway! I live in Ringwood and have colleagues in Bournemouth and Poole and they have over an hour LONGER commute than me on London days.
I have a 25 min drive to the station, then the 7.08 gets me to Waterloo for 8.20, or the 7.38 is just as fast. My colleagues get on the train over an hour earlier than me and spend an hour stopping multiples times across the New Forest!
Brockenhurst would be amazing for the train but £700k won’t get you much and I think there is less to do there for kids so if you commit to the Parkway option for the train, it’s then just a case of deciding how far you want your husband to drive.
Ringwood would be the closest- 15/20 min drive to Bournemouth airport, lots of shops, cafes, good schools, community feel e.g carnival and town events. Romsey is very similar but probably much bigger and you could get more for your money, particularly on the outskirts (though less walkable to the town centre than most of Ringwood). Your husband’s commute would be more like 45 mins but you’d also be close to Southampton if you want access to a city. Both good market towns basically.
There is also Totton and surrounding villages. It doesn’t look “cutesy”, definitely not a market town or as “naice” as Romsey/Ringwood but plenty of families and schools and really well located- you could jump on the train at Totton or Ashurst, it’s right of the edge of the New Forest, easy access to the A31 for your husbands commute and if you will have teens then buses/trains into Southampton for them. As a kid I could be out on my bike in the Forest one day and on the bus into town the next. Your budget would go much further for a house too.