I think something like an apart-hotel would suit you, there are the facilities of a hotel with self catering option in your rooms (typically two ring hob, sink, fridge, cooking and eating pans, crockery, utensils, glassware, cutlery; and kettle, toaster, iron and so on. You can often choose what level of board you want, B and B, half board or full board using their restaurant, or just pay as you go with meals.
Take a pushchair that is comfortable for a little baby to sleep in with good sun protection, and a sling is handy for boarding the plane and at the other end while you wait for the pushchair at baggage reclaim. Take a blanket in case evenings are cool/ for the airport boarding and so on. Remember you will need to take a carseat if you plan to hire a car. Most airlines will allow you to take two of three items free of charge, e.g. pushchair, car seat, travel cot. The third would be charged for. This is even if you haven't paid for a seat for an infant under two.
You will need feeding and sterilising stuff and formula if bottle feeding, with a bottle brush, and a container for the sterilising fluid and bottles. Breastfed babies are easier in that they don't require all these things.
You can book a cot/travel cot to be supplied in your room. Take some cot bedding of your own if you want, but make sure it doesn't get taken away when they change your bedding.
Take clothes, nappies and toiletries, and baby suncream. There may be laundry facilities at your chosen place, if not a tube of travel wash takes no space and you can hand-wash the baby clothes so that you won't need to take loads. Nappies can be expensive abroad so try to take one pack with you. A few toys would be handy as well, especially ones that attach to the pushchair and won't get lost. A few sachets of Calpol are handy to have in case of emergency, and insect repellent.
Use your changing bag as your hand luggage, and use it for the baby things, remember to pack spare tops and shorts for yourself and your partner in his hand luggage in case of baby sick accidents, so you can at least change!