There's nothing to fear from attending a service where the remains are to be cremated as mourners are not present when the coffin and its contents are consigned to the incinerator.
Also, please be assured that you won't be assailed by the odour of burning flesh or confronted with the sight of smoking chimneys as modern-day incerinators are fired by natural gas or propane which emit very little odour or smoke. As all cremations are completed on day the services are held, your SIL's remains will be reduced to ashes shortly after the final prayers/goodbyes have been said.
If the funeral service is taking place at one of the chapels in the grounds of the crematorium, which are usually situated in a large municipal cemetary, you'll find that the chapels are little more than rooms of varying sizes which bear scant resemblance to a church environment. They are equipped with sound systems through which the chosen hymns/music is played and it is not necessary for the service to be conducted by a vicar, although your PILs may have chosen an ordained minister or priest to officate.
The demand for cremation is such that, unless additional time has been booked, it's probable that the service will not last much longer than half an hour, after which the mourners will depart through the entrance they came in while the coffin will remain in situ and be removed to the crematorium when the last of the congregation has left the builiding.
The chapel will then be made ready for the next service and it's not uncommon to see a hearse preparing to unload its content as you emerge from the building - at those crematoriums that have more than a couple of chapels/place of worship there can be a veritable queue of hearses intent on the same purpose.
In some chapels the coffin is placed on a stationary raised conveyor belt which, at the press of a button, despatches it to the crematorium in a similar manner to the baggage carousels that can be found in airports, and you may find it disconcerting if the coffin begins to move to its final destination before you have opportunity to leave. The slow progress of the coffin towards a discreetly disguised large hole in the wall can signal the end of the service.
At one funeral I attended the coffin was placed on an elevated dais and a pair of velvet curtains were lowered in front of it as the service was concluded. I half expected the curtains to be raised so that the deceased could take a final bow.
A piece of ground is set aside for a display of the wreaths/flowers that accompany the coffin/funeral cortege to the crematorium. In common with those others who will be cremated on the same day, your SIL's name will be prominent in the space allotted to her and that those attending can view the floral tributes that have been sent to her, contribute any they may have bought with them, and take photos if they wish to do so.
After the service your PILs will no doubt want to collect any memorial cards and other missives attached to the tributes as they will be disposed of at the end of the workling day to make way for the dear departed who are to be cremated on the following day. I suggest you take a camera in case your PILs don't think to bring one but, unless you are specifically asked to take photos, I would advise you to make it available to your dh.
Unless specifically requested to wear black, mourners wear their clothing of choice. Many nearest and dearest of the departed ask that mourners dress in bright or favourite colours of the deceased. If you are not made aware of any specific dress code I would suggest you wear black or dark grey/navy blue as wearing sombre clothing continues to be viewed as a mark of respect, particularly by the older generation.
A Church of England funeral service has none of the ritual of Catholicism or the rites of the Eastern Orthodox Church and you may find it singularly unmoving, but a well-written and read eulogy may provoke an unexpected torrent of grief for the SIL you barely knew. Take tissues and dole them out to others if you have no need of them.
I always take a hip flask bottle of clear nail varnish to funerals, as I invaribly encounter someone in the Ladies who's also managed to ladder her stockings/tights and ,a packet of small safety pins to spare the blushes of those who, having scoped out the attire of their fellow mourners, decide that the plunge neck navel-grazing top isn't as suitable as it appeared earlier.
If one of my siblings were to die prematurely I would want and expect my SO to take a back seat before, during, and after the funeral service so I could give my undivided attention to my dps but if your dh customarily relegates you to the back seat, or continues to do so after your SIL's ashes have been scattered/interred, I suggest you create another thread on this board to raise any concern or gripe you may have at being treated like a second-class citizen in your marriage.