I can see your problem. Tenders are always a compromise and in you case the tradeoff is between having the capacity to carry all your payload in one go and your ability to handle and stow the tender on board. If you are unwilling to compromise on the payload then you have to deal with the inconvenience of the size. To me the only sensible solution in that case is davits which will allow you to stow the dinghy complete with engine - although if I were going this route I would buy a RIB as you no longer need the benefit of deflating and stowing in a locker when not in use. This is just the sort of solution many cruisers in the Caribbean use where the requirement is for a tender capable of carrying large payloads (stores, water, people) long distances (boats are at anchor most of the time) in a regular basis. RIBs in the 3-3.5m range are the most common.
However if you are marina based in the UK and only use the dinghy for odd trips ashore then you really have to question whether the cost, inconvenience and difficulty of stowing is worth it compared with doing 2 journeys ashore with your payload. The 3m I suggested would take all your family (but probably not the dog if it is like my Lab!), but if you want to take a lot of gear as well just make two journeys. With a 5hp you will be able to plane so getting back for the second lot of passengers will be quick. The benefit is you don't need davits, although you might want a crane for the outboard, and for long passages it is easy to deflate and stow in a locker or down below. If you are on a mooring rather than in a marina berth, I can see the need for a larger tender to get you all out to the boat in one go, but in this case I would have two boats - a bigger one, probably a hard dinghy to be left on the mooring and a smaller inflatable stowed in a locker for use when cruising.
Although the 3.8m is relatively light compared with a smaller RIB you will find its bulk (length and particularly beam) a real challenge. Imagine lifting a boat that size with a halyard over the guardrails, either vertically or horizontally with a bridle and trying to stow when there is limited room (even worse if there is any wind blowing). Lifting it on slings on the transom is a possibility, although its size means it will dominate the stern, shut off rear visibility, increase windage and overhang significantly either size. Suspect the ends of the tube may be under water when sailing heeled. If you do go down this route you can use the topping lift if you have a rigid kicker, or if you have a split backstay you can attach a block at the split for a dedicated line. This is the arrangement I had on my 37 for the pasarell.
Sorry if this sounds negative, but if you look at other similar sized cruisers you will find the dominant tender size is in the 2.4-3m range. The only negative of this size is the limitations of payload, but when you think of the number of times a year this might be an issue, you may think it is an easy compromise against all the negatives that come with larger dinghies.
