I doubt that you'd have any issues entering with your family, if you just say you're on holiday for a month. They shouldn't have any reason to doubt you, especially if you've got previous UK entry/exit stamps in your passport. I've been in and out of the UK about 1-2 times a year for the past four years and only ever had an issue with a UK border agent once - at the Gare du Nord EuroStar railway terminal in Paris, where we went through the line seperately (lesson learned!).
Thanks, that's very reassuring! I'm starting to feel so backed into a corner by all this that I'm more and more willing to take the risks.
I'll be honest, I would not recommend doing this.
From experience of advising on the forum for the last 11 years, I would say that a one-month stay with your kids and husband, who will not be returning to the US with you, plus no job or home of your own to go back to, would be a BIG red flag and I would advise against trying it.
Visiting the UK for a short, temporary visit, when you have a family, job and home back in the US, is usually fine, but staying for 1 month, with your entire UK citizen family who are moving to the UK in tow, when you don't have a spousal visa yet, is entirely different.
The reasons they would have to doubt you:
- your husband is moving to the UK, so you may be tempted to stay with him and not return to the US
- your 'job' is a stay-at-home mom, but your kids are moving to the UK, so you won't have a 'job' to return to in the US and may be tempted to stay with them and not return to the US
- you've just sold your home, so you have no home to return to, so you may be tempted to just stay in the UK and not return to the US.
Your only saving grace might be your pending spousal visa application, but since as far as we can tell you aren't really supposed to enter the UK while it is pending, that could be a dodgy reason too (i.e. you might have issues being allowed in if you mention it, and/or you might be tempted to just not bother returning to the US to pick it up).