SLOW internet access; how to fix?

So...since the stake combined our branch's Primary and Youth classes with the full-sized ward that uses the same chapel. During the two hours our branch and this ward are combined, the internet on the clerk's computer is very slow. I'd like to fix this, so as to be able to do the clerk stuff I need to do.

How can I do this? New Router? Limit wifi usage/bandwidth?

How many people need to approve this change?

You should ask your STS to check bandwidth usage in your meetinghouse on Sundays. If it looks like members are streaming video during meetings, then all ward council members that share the meetinghouse should be trained how to download the videos they need at home, rather than streaming them.
If bandwidth usage is not very high, then you are probably using a DSL modem with a low usage cap. Your FM tries to reduce his expenses by selecting the lowest bandwidth that will satisfy the needs of clerks and FHCs. He does not want to pay more for the ability to stream videos.

Talk with the STS. He can monitor the bandwidth via TM. He can then ask the stake president to talk to FM about raising the bandwidth. However, it's possible that you're already at the highest plan that's available for the chapel. You might be in a "hole" where high speed services are not available. In that case, you need to talk to the STS about limiting the number of access points to only cover certain areas.

If you're being assigned a lot of things that need to be done during the Church meetings, I'd talk to your bishopric and others who are requesting reports and ask them to let you know what they need beforehand, or be prepared to get what they need after Church or during the week. While it may happen occasionally, nobody should be asked or expected to miss their Sunday school and/or priesthood meetings every week; especially ward leaders, who are expected to set the example for members who struggle to attend.

Go in at some other point and do the work. Only the tithing processing and a few occasional other things are needful during church hours. Most of the stuff make a written list and deal with it some other night. Being ward clerk is one of the highest work load callings in the church and I understand the desire not to need to live at the church. But in the last 3 years so much of it you can do from your home anyway. Tithing load is down and most of the callings, reports, and membership/address correction stuff you can do anywhere you have secure internet access so there is far less need to be at the church. Then work on training so your secretaries can print many of the reports they want now so you don't have to do it. The bishop and the executive secretary may not make class very often but everyone else mostly should.(ideally even they will but it seems to be rare)