Kargatorfan, first let me say how very sorry I am. This is the hardest part of sharing our lives with our furry friends.
I have stood in your shoes too many times, and from my experience:
I have always felt it very important to stay with my friend through the end. My touch, my voice has made the process easier for my dog - which is the most important thing. The only important thing.
I prefer that the vet uses a sedative first, so that when the final drug is inserted there is no pain. This is the usual method here in Switzerland but one should discuss this first with the vet.
Most vets will do a house visit, usually charging for traveling costs in addition to the regular fee. But the costs are not much, and if that is what you prefer well worth it.
Do I remember that you have a second dog as well? If so, please think about how you want to handle this in a home situation. It is often recommended that the second dog not be present during the euthanasia, as you want to be focused on your poor beagle - but that afterwards the second be allowed back in the room to sniff the body of his/her friend, so that there is an understanding that the friend is indeed gone.
However, this very much depends on the relationship the two dogs have, on the sensitivity of each dog. But do think about that aspect.
One thing to be aware of if you choose euthanasia at home: it is common for the bladder to release urine upon/after death. You might want to place your dog on a washable blanket so that you can cuddle him in the last moments.
I had planned euthanasia at home, but circumstances haven't worked out that way. Even so, euthanasia at the practice has also been a gentle, comforting experience. (As much as can be.)
Most of the time I have had my general practice vet perform the euthanasia rather than have it done at Hünenberg or the Tierspital, even though we were seeing specialists at the end. This is because the smaller practices are a low key atmosphere, which I felt was best. One time was at the Tierspital, and even under such circumstances I must say that the vet handled it with all the empathy and kindness one could wish for.
For your sake, I would suggest that you make an appointment with your local vet prior to the euthanasia - just you if you don't want your beagle to go through the stress of the visit. Speak with your vet about the process, decide what you want done, what you don't want done; you will feel better if prepared.
I know that the good folks at Hünenberg and the Oncology Center kept in touch with my vet throughout my dogs' treatment; when it was time no one questioned my decision. Most vets here are very sensitive, understand that the person best able to make the decision is the owner.
When possible, my vet schedules euthanasia at the end of the day, when no one else is around. This way you may take all the time you need, before and after.
I have always opted for cremation. My vet arranges this; most do as well if that is what you want. You can have an individual cremation where you get the ashes back, or opt for cremation in a group. The latter is less expensive. When group cremation is done, I know that Schaffisheim scatters the ashes in their memorial garden, a lovely gesture - I don't know what other animal crematoria do, but you should ask if that is an issue for you.
If you opt for individual cremation you may also ask for the ashes back to keep or scatter yourself. I chose to scatter the ashes of one of my dogs on one of his favorite mountain trails.
If you wish to organize a cremation yourself you may do so - call the crematorium ahead of time so that someone is scheduled to receive your dog's body.
The cost of cremation will vary by body weight, and whether it is an individual or group cremation. Expect something in the order of CHF 200 for a group cremation, 400-600 for individual, including the urn. Less if you don't want an urn.
As to burial - if you are renting this is problematic, you'd need the landlord's permission. Whether burial is allowed or not is a Gemeinde matter; many Gemeinde do allow it but only for animals under 10kg as another poster mentioned - and only if the property does not lie in a green zone, landwirtschaftszone, or other protected area. Check with your Gemeinde as to the specific rules if this is an option you wish to pursue.
It is good that you are thinking about this now, while your head is still clear. It is often a good idea to discuss all this with the vet beforehand so that he notes your wishes - because the emotion of the moment makes it difficult to do much clear thinking or decision making.
Again, I am so very sorry - you have my heartfelt sympathy. I wish you and your family strength in the days ahead - but be at peace that you are doing the right thing for your dog. It is because we love our four footed friends that we do not allow them to suffer.
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