Hi TheNewWife!
In the UK, induction means one, two or all of the following: vaginal prostaglandins (gel, pessary or tablet), breaking your waters, then an IV oxytocin drip (syntocinon or "synt", called pitocin or "pit" in the US). A stretch and sweep isn't really counted as induction.
I don't know what the case is in your country, but I'd bet they will insist on constant fetal monitoring with a CTG, because oxytocin drips give stronger/faster contractions which are more likely to distress the baby. CTGs can sometimes be done in water, but oxytocin almost always can't. The doctors will assume that if you sign up for induction, you're signing up for any/all that is necessary to get you into labour and deliver your baby so if you want a bespoke plan, e.g. One that doesn't involve a particular element, you should make that clear ASAP.
Just occasionally, consultants may agree to trying a pessary and if that gets you into labour with nothing else, agreeing not to do constant CTG monitoring. But that's rare in the UK - I don't know about where you are. This is the main issue though, because CTG monitoring is known to increase unnecessary intervention.
I'd echo a lot of what has been said: Induction can work just fine, and IMHO it certainly has its place, but when there is a good reason. Personally, I have to say convenience in terms of family travel wouldn't be one of those good reasons if it were me, but that's a choice only you can make. If you'd had a quick and trouble-free previous labour and it was likely to be a matter of just "lighting the blue touch paper", it might be different, but it can be pretty difficult getting a first time mum into labour, and would definitely be a step away from a natural water birth if that's what you want.
Good luck, whatever you choose. 