If first-order hybrids made up only a small proportion of the total population of humans and Neanderthals, then the probability that a pairing between a member of a modern human tribe and a member of a Neanderthal tribe would involve a first-order hybrid is quite small. Like if there are 2 hybrids in a 150-strong tribe at the frontier, and a cross-tribe pairing happens, there is about a 1.3% chance that it involves a hybrid, and half of that that the gender matches up. Even with a higher estimate of 5% hybrids in a tribe, it's a 1.67% chance for a match with the right gender.

And when that chance is realised, and a second-order hybrid is produced, the high child mortality rates of the time would put downward pressure on their numbers. Not zero, but a couple of orders of magnitudes lower than first-order hybrids.

First-order hybrid being having one parent from a Neanderthal tribe, other from a human tribe. Second-order hybrid additionally having at least one parent as a first-order hybrid (as in your step 3).

Also, there actually is Neanderthal DNA in the modern X chromosome. If in your step 2, Ann gives birth to a daughter Andrea, the daughter would have a Neanderthal X chromosome, and she can pass it on within her tribe. But she would have no Neanderthal mtDNA, which is only passed on maternally.

But there is other data that this model does not explain. Like, why is there no Neanderthal contribution to the modern Y chromosome?