Extnding dependent stay by 5 weeks

I am currently on a government Authorised Exchange visa (Temporary Work) – tier 5 working at a UK university on an academic sabbatical. I am employed at an American University and have lived in the USA for 15 years. I hold a resident green card in the USA, but am a french national.

My husband is also on a temporary work visa in the UK at the same UK University under a Fulbright agreement. He is American, employed at the same american university as me.

When we applied from the USA for our UK visa, I applied on behalf of our two young children as dependents on my visa using their french passport (they are dual citizen, France/USA).

Here is the issue: my VISA expires July 31st 2024, while my husbands' visa expires June 22nd 2024. Back when our VISAs were issue in July 2023, we immediately noticed that our kids visa's expired on June 22nd, while I had requested July 31st. After months of back and forth with UKVI which started in July 2023, they pulled out the following rule: "SW 36.2. A child will be granted permission which ends on the same date as whichever of their parents’ permission ends first, unless both parents have (or are being granted) settlement or British Citizenship, in which case the child will be granted permission for 3 years."

How can I extend my children's visa deadline to match mine (we're talking about a 5 week extension)? I won't ellaborate too much but the kids needs to finish their school year in the UK, my husband will be in remote alaska doing field work in June/July with no possibility to care for our kids, and even if he did, our house is rented out in the USA and they have no place to stay in the US until July 31st...

Is it reasonable for me to go to france around June 22nd with my kids and have them re-enter as visitors in the UK? It seems re-entry for my kids would dependent on a border agent's mood and I don't want to gamble. Or is there a proper way for me to request a short extension for my children?

Any help appreciated, thank you so much.

There is no easy solution that will encompass all the loose ends in your circumstances. The least risk is just to carry on as normal and leave the kids in school, you carry on in your role and when it is time to leave, head back to the USA.

If you leave the U.K. and return as suggested then you increase the risks, a 5 week overstay for minors under the age of 18 is disregarded in any event. In fact and overstaying by minors is disregarded.

Sometimes the do nothing option is the best. Is it right, no, but is it worth trying to do the right, in this case probably not.