It would take forever to get dressed and, obviously, undressed as well.

This is not actually true. The videos you're seeing (assuming that they're the same ones I've seen) are not exactly inaccurate, but they take certain liberties - namely, they are made to show you the process, which necessitates moving more slowly and deliberately to let you make out the movements, and have to be aesthetically pleasing. It would be a mistake to take them to be completely perfect in every respect, or to be completely objective representations of getting dressed. In reality, with the practice of dressing every day and not needing to impress anyone while doing it, women would be able to go through the routine in a brisk, businesslike manner.

It also seems that most women who would wear this fashion would likely have a hired girl to help her get into and out of it.

Not really, or rather, not necessarily. The layering issues you're describing would be true for women of just about any social class during this period: they all wore shifts/chemises, corsetry, and petticoats. The eighteenth-century skirt supports like pocket hoops were more of a wealthy fashion, but by the time of the industrially-made hoops and bustles of the mid-to-late nineteenth century, all but the poorest could afford something. Through the eighteenth century, all but one specific type of short-lived high-fashion gown (and court dress across the continent, and British court dress until about 1740) fastened in the front; reasonably fashionable women's day dress fastened in the back in most of the first half of the nineteenth century, and the finest evening dress tended to continue to do so through 1900, but many women would continue to wear dresses they could fasten easily themselves. The real issue was the lacing of the corset, which was a somewhat lengthy process until the split busk, which allowed it to pop open in front, became commonly used in the 1850s - and there's something of a fixation with women's inability to do that easily for themselves in pop culture and scholarship in the twentieth century and today, but the reality is that hardly any women lived entirely alone, as many do now. Younger women had sisters, mothers, aunt, grandmothers; married ones had husbands, daughters, mothers- and sisters- and daughters-in-law. Servants were also not solely the province of the very wealthy: wages for labor were very low, so even quite modest families might employ a single maid-of-all-work who would be able to lend a hand when needed, if there was nobody else to help at the time. Women who were so poor that they couldn't afford any servant and so alone that they had no family to live with would typically be so far from respectability that it would not matter so much whether they wore a corset.

Did women have attire that could be worn around the house in front of her husband that did not involve a laborious process to put on?

Yes! Most women in the eighteenth century would have a "bedgown", a very loose jacket with no fastenings, made of silk, cotton, or wool depending on need and budget - this could be put on over a shift and petticoat to wear before going to bed or immediately after getting up or when ill (and for those very poor women I mentioned earlier, this might be their only upper-body garment during the day). There are also late-eighteenth-century fashion plates showing that at least wealthy French women had peignoirs, even fuller jackets with loose sleeves gathered up at the wrist, usually made of very lightweight fabric. Wrapping gowns existed as well, essentially knee- or floor-length bedgowns, and they continued to exist through the nineteenth century, altering as needed to conform to fashion.

The teagown of the late nineteenth century was essentially a high fashion appropriation of the unconventional dress of the Aesthetics, a group that rejected various aspects of fashion like corsetry, skirt supports, and tight sleeves - these could be worn in the home around teatime, even if guests were invited to call. Although these were sometimes made with stiffening themselves to help keep a certain amount of shape, they could be and often were worn without corsets.

If a woman wanted to have sex with her husband, what was that process like? Would he undress her (or she undress in front of him) like is commonly done today, or was there a more elaborate process? Did couples even sleep together at this time? Was there ever any sporadic sex or was it all ceremonial and formal?

I finally get to the meat of your question! It has to be said that for this entire time period, it would be technically possible for a woman to have sex without taking off her clothes: as I discussed in this answer, bifurcated undergarments that were actually closed between the legs were not really common until the twentieth century. If a couple were completely overcome with passion while alone in a drawing room, they did not need to fully take off any clothing. (And, as discussed above, even if they did want to have sex without clothing during the day, they would certainly have been able to manage to get out of their clothing fairly easily. Another Period is a funny show, but this scene is more funny because it turns an operation like "undoing one button on a petticoat's waistband" or "undoing a row of hooks" into a team effort.)

But how often would married couples go from zero to sex? While premarital sex happened in all kinds of places depending on when couples could get alone time, marital activities seem to have generally been done in the marital bed. It's hard to find direct evidence of this, at least in the sources I have to hand, but the fact that women who wanted to avoid their husband asserting his conjugal rights (i.e. marital rape) often achieved this by avoiding the bed - by having their own bedroom, by staying up late with work, by sleeping with the children - implies that most sexual activity would be expected to happen there. (Separate bedchambers were the norm for the upper and upper-middle classes, with the wealthiest even having attached dressing rooms. I can't say exactly how far down the social scale they continued, but the working classes definitely shared beds and bedrooms.) In these cases, women and men would have already undressed and be in nightclothes, so the point is rather moot. There was no ceremony for getting undressed: the wealthy might be undressed separately by servants and put into their nightclothes, then meet up again, but there was no requirement to do that rather than undressing each other - it's just that you generally want someone who knows what they're doing messing with your expensive evening dress.