The 6-month EEA Family Permit is what you should apply for. It's really your only feasible option as you'll need get one before you leave the US in order to be allowed into the UK as the spouse of an EEA citizen.
Once you have arrived in the UK on the EEA Family permit, you can then apply for a 5-year EEA Residence Permit.
You should not purchase plane tickets before a visa is approved in case you can't travel and lose the money from the ticket. Often it can be cheaper to purchase a round-trip ticket and just not use the return leg.
However, as you already have the automatic right to live and work in the UK with your husband, providing he is exercising his EEA Treaty Rights (either looking for work or has a UK job), it should just be a formality and there shouldn't be any reason for it to be refused - it's not even technically a visa and is about the easiest thing you can apply for.
He doesn't need to actually have started working yet - his job contract is fine. You could even apply if he was simply looking for work and hadn't secured a job yet.
You don't need to send your husband's actual passport with the application (it's not recommended to do this anyway as he may need the passport), just send a certified/notarised copy of his passport photo page.
All you should need to provide for the application is:
- Your passport
- Passport photo
- Your original marriage certificate
- A certified/notarised copy of his passport photo page
- Evidence of his job in the UK (original job contract) to show he will be exercising EEA Treaty Rights
- Evidence of your intended accommodation in the UK (although this is not actually a requirement for the permit)
On the other hand, I could just go to Heathrow and get the 3-month stamp, and then apply for a Residence Card, yes? I'm not going to run into problems entering with a one-way ticket, am I (especially if I'm accompanied by a Dutch dependent)?
This is not a good idea because to enter as a visitor, you would have to prove you are only a tourist with no intention of living in the UK and that you will return to your life in the US within 6 months and a one-way ticket is a massive red flag.
You would need to have a return ticket, evidence of a job and a home in the US to go back to (letter from your US employer and evidence of homeownership or rental agreement in the US) and enough money to support yourself without working for the full trip.
There is no 3-month stamp though... visitor visa stamps are usually issued for 6 months, though the immigration officer can technically only stamp you in as little time as he likes.
Is the 3-month stamp enough time to get the Residence Card process started and my status legalized? What legal or ta
Technically, there's nothing illegal about applying for the residence card while in the UK as a visitor, however, the chances of you actually being allowed to enter the UK as a visitor in your situation are pretty slim because you have to prove you will NOT be living in the UK... it that won't look good if you have a Dutch husband living in the UK, a Dutch child entering with you and you have packed up your life in the US to come to the UK.
Also, if you were allowed in as a visitor, you would not be allowed to work, you would not have access to NHS care and you would not be entitled to claim any UK benefits.
If you apply for a free-of-charge EEA family permit first though, you won't be a visitor, you will be able to work, you will have free access to the NHS and you will be entitled to claim benefits.